Celtic's second came 10 minutes after the restart and with a big slice of luck as Baram Kayal's strike from the edge of the area deflected off Stefano Denswil and past the keeper.
The hosts suffered a late shock when Nir Biton was controversially shown a straight red card just 11 minutes after coming on, but they held out for the win despite a late goal from Lasse Schone given Ajax a glimmer of hope.
You can read how an electric night of Champions League football at Celtic Park unfolded with Sports Mole's live coverage below.
6.45pmGood evening! Thank you very much for joining Sports Mole for what promises to be an exciting match between two sides with a grand history in the Champions League, as Celtic take on Ajax.
6.47pmWe'll start by looking at out hosts for this evening's game, and while their European pedigree is not among the best nowadays, there are few sides who can match the home atmosphere of Celtic Park on a European night.
6.49pmCeltic are certainly not of the same class as some of the other teams in this competition - or even in their group - but their home ground gives them a fighting chance against the very best. That was shown last season when they beat Barcelona here, and they almost pulled off another result against the Catalan giants in their last outing, only to be beaten by Cesc Fabregas's late header.
6.51pmCeltic will be look to the home fans to give them a much-needed boost, then. Manager Neil Lennon has dubbed this a "must-not-lose" match, and even a draw would leave them with a mountain to climb if they want to reach the knockout stages. Certainly, with the likes of Barcelona and AC Milan in your group, every point that you can take off the likes of Ajax will be invaluable.
6.53pmProgression from the group may be a step too far for the Bhoys, given the quality of competition, but they will certainly have one eye on sealing third to place to at least guarantee some European action after Christmas. The team that finishes third will be entered into the Europa League and, unless either of these sides can pull off an upset, it looks like being a straight shoot-out between them.
6.55pmNumber one on the priority list for Celtic right now, though, is to score a goal. Not only do they have no points to their name so far - although there has been no shame attached to their two defeats - but they also do not have a goal to boast about either. Tonight is the best chance that they will get in this group stage to pick up there first win but, to do that, they need to find their shooting boots.
6.57pmCeltic don't come into this match in great form, however. Such is their dominance over the domestic game - especially since the collapse of Rangers - that they are expected to win almost every match in the league and cup. However, they have only won three times in their last seven matches in all competitions, including a 1-0 defeat after extra time to lowly Greenock Morton in the Scottish League Cup a month ago.
6.59pmStill, a Celtic in what, by their standards, is wobbly form still lead their domestic table by four points having not tasted defeat in their opening nine matches. Even more encouragingly for Celtic, they have a game in hand over second place Inverness, so you would expect them to extend that gap to seven.
7.01pmI have already mentioned Celtic's formidable home presence, and there is no doubt that teams find this a tough place to come to, particularly on European nights. However, the Bhoys have lost two of their last three games at Celtic Park. Perhaps there is something to read into about how special European nights are here that they lost to Barcelona by the same scoreline that they lost to Greenock Morton by.
7.03pmThe only sides who have beaten Celtic here in the Champions League since 2009 have been Juventus and Barcelona. Compare that to Ajax's away record in the competition, and Celtic will be confident ahead of tonight's match. Ajax are without a win in their last five Champions League away matches, a run that stretches all the way back to their 2-0 win over Dinamo Zagreb more than two years ago.
7.05pmAjax's away form when you include domestic matters isn't much better either. They have not won any of their last six matches on their travels, a run that includes two back-to-back 4-0 defeats at the hands of Barcelona and PSV respectively.
7.07pmTheir general form is better than that, however. They are unbeaten in their last five in all competitions, responding to those heavy consecutive defeats with three wins - one of which was a 6-0 triumph - and two draws. It could have been even better than that had they held out against Milan in their last Champions League match too. The Dutch side took the lead in the 90th minute, but a penalty from Mario Balotelli clinched a dramatic point for Milan.
7.09pmAjax have similarly high standards in Holland to those that Celtic demand in Scotland, but the current campaign has been a rather topsy-turvy one for Frank de Boer's side. They sit fourth in the Eredivisie table, although that disappointing position is tempered by the fact that they are just one point off leaders Twente and are one of three teams on 18 points from 10 games.
7.10pmTheir performance in the Champions League has been similarly erratic, as they followed up a 4-0 drubbing by Barcelona with that highly respectable draw against Milan. They will still have high hopes of qualifying, especially given Milan's current injury-ravaged state, but matches like this one tonight are simply must-win games for them if they are to usurp the big two.
7.12pmOf course, 'the big two' is a highly complimentary term in a group full of European giants. This season's Group H is the first time that four previous winners of Europe's premier competition have been drawn in the same group, and Ajax's glory days can rank right alongside Barcelona and Milan as some of the greatest days in the European Cup/Champions League's history.
7.14pmThe Dutch side were the team at the start of the 1970s, winning three consecutive European Cups and alerting the world to 'Total Football' in the process. Celtic also made history when they won the competition back in 1967, becoming the first British team to claim the crown. The 'Lisbon Lions' beat Inter Milan in the final, and their squad was notable for the proximity in which each of them grew up to Celtic Park.
7.16pmTEAM NEWS: Right, the team news is in from both sides, and the good news from Celtic's point of view is that Lustig has been passed fit to play having missed the 1-1 draw with Hibernian at the weekend. Izaguirre also returns for the Bhoys, who name the enigmatic Samaras up front. Full team news coming up.
7.20pmAJAX STARTING XI: Cillessen; Van Rhijn, Veltman, Denswil, Blind; De Jong, Poulsen, Serero; Andersen, Sigthorsson, Fischer
7.20pmAJAX SUBS: Vermeer, Van der Hoorn, Boilesen, Klaassen, Schone, Hoesen, De Sa
7.22pmWhat can we make of those sides, then? Well, conspicuous by their absence in the Celtic side are captain Scott Brown and Kris Commons, both of whom will be sorely missed by the hosts tonight. One missing is bad enough, but to have both of them ruled out - Brown suspended for a petulant kick on Neymar and Commons injured during the match against Hibernian at the weekend - is a real blow for Neil Lennon.
7.24pmLustig's return is an advantage for them, however, as is Ledley appearance back on the bench following a lengthy absence. Lennon is evidently keen to ease him back to match fitness, but he could be forced to call upon the midfielder earlier than expected if things aren't going Celtic's way tonight.
7.26pmUp front they will be looking to Samaras to break their duck in the groups this season. The Greek striker can be hugely frustrating at times and probably wouldn't cope in a league of higher quality than the Scottish Premiership, but he does seem to relish European nights. He can sometimes go missing in matches, but at his best he is a real handful. At the other ends, Forster certainly had his hands full against Barcelona a few weeks ago and he almost kept a memorable clean sheet in that match. He will be hoping for a similar personal performance - but a different team result - tonight.
7.28pmLooking across to the Ajax lineup, and they have also been boosted by a returning defenders as Van Rhijn passed a late fitness test to be included. Christian Poulsen will be familiar to English fans from his days at Liverpool, and it will be up to him to protect the Ajax back four tonight.
7.30pmIn an attacking sense, Siem de Jong is the main danger for the visitors. The playmaker has carved something of a name for himself on the European stage, and he will be looking to take advantage of the absence of Scott Brown this evening. Icelandic forward Kolbeinn Sigthorsson will be the biggest threat to the Celtic goal, having scored six times in 10 appearances so far this season.
7.32pmAjax boss Frank de Boer also deserves a mention in this. He will have found memories of this part of the world - although perhaps not Celtic Park in particular. Expect a big negative reaction to the Dutchman from the home fans due to his time as a Rangers player. While it will not endear him to the Celtic fans, his time in Scotland will have given him ample experience of exactly what his side are in for tonight. If anything can match the atmosphere in a Champions League fixture at Celtic Park, then it is an Old Firm derby, and De Boer knows all about them.
7.35pmPREDICTION: We're 10 minutes from kickoff at Celtic Park, which can mean only one thing - it is prediction time! This one is a tough one to predict as both sides will go into it with realistic hopes of coming away with all three points. The home advantage for Celtic should not be underestimated, but the Bhoys are also missing two of their most influential players, including their regular captain. A draw would satisfy no-one, but I think it is the most likely result tonight. I'll go for 1-1.
7.37pmI have already mentioned the illustrious history of both these sides in this competition, but Celtic in particular have plenty of recent experience in the Champions League. Tonight will be their 21st game in the competition in the last 15 months. Ten of those have been in qualifiers, nine in groups and two in the knockout rounds against Juventus.
7.39pmThese two do have a limited history of meetings. The last came back in 2001, when Ajax triumphed here in a Champions League third qualifying round. However, Celtic had won 3-1 in the first leg, putting them through 3-2 on aggregate.
7.41pmChampions League nights are always special, and you can follow every match live with Sports Mole tonight. The commentaries we have on offer can be seen here, while I will also be doing my best to keep you up to date with major events from around Europe as and when they happen.
7.43pmThe Glasgow roar greets the players as they stroll out of the tunnel, while a rousing rendition of 'You'll Never Walk Alone' has also just finished from the home fans. Cue the inimitable Champions League music for the volume to crank up even higher ahead of a vital game for both sides.
7.45pmThe referee for tonight's match is Croat Ivan Bebek. He oversees the handshake between the two captains, and it is Samaras who wears the armband for Celtic in the absence of the suspended Brown.
1 minKICKOFF: Here we go then. Celtic get us underway in what could be a must win for both sides if they are to keep their qualification hopes alive.
3 minSamaras makes an early foul on Serero, but curiously the referee doesn't even award a free kick. It was a poor challenge, and Samaras is perhaps lucky not to pick up an early booking there.
5 minAjax have settle into this match quickest, but Celtic are the side who look to have more impetus about them. A low cross has just been cleared behind for an early Celtic corner, but it comes to nothing for the hosts.
7 minNothing to speak of in terms of an Ajax attacking threat so far. They have seen plenty of the ball, but are playing patiently at the moment and don't seem keen to force the issue in the opening stages.
9 minUPDATE: Plenty of early drama from around Europe. Chelsea have already taken the lead against Schalke through Fernando Torres, while Atletico Madrid lead Austria Vienna through Raul Garcia. Meanwhile, in Portugal, Hector Herrera has already been dismissed having picked up two yellow cards in the opening six minutes.
11 minNervy moment for Forster as he spills what should be a simple save from a deflected cross. The ball squirms out of his grasp and he is forced to kick it away with two strikers bearing down on him.
13 minUPDATE: News from the other match in Group H coming through, and it isn't good news for either Celtic or Ajax. Milan have taken a surprise lead against Barcelona, with Robinho making it 1-0 to the Italians.
13 minBack in Glasgow, Samaras pings a superb ball to Stokes, but he runs straight into a defender with only one man to beat. The hosts work it back into the box, however, and Pukki just can't get enough on a low cross to turn it goalwards.
15 minNice football from Ajax as they work their way into an advanced position with a string of quick passes. De Jong eventually collects the ball on the right and tries a low cross into a dangerous area, but he gets it too close to the keeper, who makes a simple interception.
17 minUPDATE: Arsenal are facing arguably the biggest threat to their fine recent form tonight, and sure enough Dortmund have taken the lead at the Emirates.
19 minCeltic are beginning to turn the screw in this one now. They have had the better of the last five minutes or so without creating a really good chance, but they do look capable of finding a breakthrough.
20 minUPDATE: Diego Costa just can't stop scoring for Atletico Madrid, can he? The Brazilian-born striker is on the scoresheet again tonight as he extends his side's lead over Austria Vienna to 2-0.
21 minAjax have their most promising moment of the match so far, but Fischer completely wastes it. He was found by an incisive pass from the right and suddenly had space in the box, but his subsequent cross - I presume that is what it was - went straight out for a goal kick.
23 minThe fans are making plenty of noise here, as expected, but they haven't had too much to cheer in terms of events on the field so far. Celtic are playing positively and they do look dangerous, but neither side have managed to carve out a good chance as of yet.
25 minUPDATE: He's back! Barcelona level things up at the San Siro, and it is the little maestro Lionel Messi who celebrates his return to the starting lineup with a goal. He just never disappoints, does he?
26 minGreat defending from Lustig as Van Rhijn's cross is just too high for Sigthorsson but looks like it will reach De Jong at the far post. Lustig slides in to make a vital interception at the expense of a corner, though.
28 minThe stadium is bouncing at the moment! The home fans are doing the 'Poznan' and generating a tremendous noise. The news from the San Siro is bound to have filtered through to them, and that will improve their mood even further. A Barcelona win is the best result for both these sides in that match as it could put them within touching distance of Milan.
30 minOFF THE POST! That is a let off for Celtic. A free kick is floated into the box and Charlie Mulgrew gets his head to it, but only succeeds in flicking the ball on to Poulsen at the back post. The former Liverpool midfielder volleyed it first time and almost caught Forster out of position, but it came clattering back off the post.
32 minPukki wins a free kick for the hosts around 35 yards from goal. The angle and the distance mean that a shot is out of the question, but they should be able to get a decent cross into the box from this one.
34 minIt is a poor delivery but finds its way to Forrest on the edge of the box. His shot is blocked and suddenly Ajax threaten to break away. De Jong is racing through on goal with only Van Dijk in attendance, but the Dutch defender makes a brilliant tackle to deny the striker a clear run on goal. He had to get that right otherwise it would have been a red card.
36 minSamaras makes good headway down the left before sending a low delivery towards the near post. It is the right ball for Stokes to run on to, but Cillessen dives at the Celtic man's feet to deny him a shot. Good, brave goalkeeping there.
38 minThings are getting a little feisty out there right now but, fair play to the referee, he is letting the game run at every opportunity. This one could become quite dull if he was blowing his whistle every couple of minutes, so that is very good refereeing from the Croat.
40 minUPDATE: Good news for Arsenal fans - the Gunners are now level with Dortmund thanks to Olivier Giroud's strike. It is 1-1 at the Emirates.
42 minForrest almost gets onto the end of a deflected cross into the box, but he just checked his run as he thought the ball was going to be cut out. Had he taken a gamble there, he would've been in a very good position.
43 minFabulous corner from Mulgrew as he swings it out and then back in right underneath the bar, forcing the keeper to tip it over.
45 minTerrific penalty from Forrest as he gets it right into the corner, beating the keeper who guessed the right way. It took an age to eventually take it after some mind games from the keeper and then handbags on the edge of the box between Poulsen and Van Dijk, which earned them both yellows. The kick was awarded when Denswil brought down Stokes and, although there wasn't a huge amount of contact, it was the right decision from the ref.
8.36pmWhat a perfect way to end the half for the hosts. I doubt anyone heard the half time whistle when it went as the place was absolutely rocking. It wasn't a half blessed with lots of chances, but Celtic were gifted one from the spot and Forrest showed composure that belied his age by tucking the penalty away.
8.38pmThat is there first goal in the Champions League proper this season, and they couldn't have wished for it to come at a better time. As things stand, they will put themselves right back in the mix in Group H, a position that would be strengthened further if Barcelona can find a winner in the second half against Milan.
8.40pmBefore the goal it was Ajax who had come closest to taking the lead. Poulsen struck the outside of the post having latched onto an inadvertent Mulgrew flick on at the back post. The former Liverpool man wasn't a long way out and perhaps you would have expected a more seasoned finisher to have scored, but he couldn't have done much more than he did.
8.42pmForster is so often the hero for Celtic in Europe, but he has been a spectator for much of the half. Ajax haven't threatened the Celtic goal apart from Poulsen's chance, and it has been a comfortable night on the whole for the Celtic defence.
8.44pmThat is not to say that the hosts have dominated this match, however. Exactly the same could be said for the Ajax defence, who also seemed pretty comfortable before that late penalty. The visitors have enjoyed more of the ball, but they will need to do more with it if they are to come back into this match.
8.46pmReferee Ivan Bebek deserves credit for his first-half performance too. In fact, he is probably the man who has performed best in this match so far! He has let the play run on a number of occasions when stricter officials may have blown, and that he ensured that the match has been free-flowing and fast-moving. The big decision was, of course, the penalty, and he got it spot on thanks largely to the fact that he was perfectly placed.
8.48pmHere is a perfect picture of Forrest's penalty, which is all that separates the sides so far. The keeper guessed the right way but had no chance given the quality of the spot kick.
46 minKICKOFF: Ajax get us back underway at Celtic Park. The visitors have a big 45 minutes ahead of them and could be all-but out of the race to qualify if they fail to come back into this match.
48 minFine play from Forrest as he makes his way down the right flank before sending a dangerous low delivery into the box that is very well defended by Denswil. That was a vital interception as Celtic had bodies in the box there.
53 minCHANCE! What a chance for Serero as he plays a one-two with Sigthorsson that sends him clean through on goal. He only has Forster to beat, but that is easier said than done and the Celtic keeper makes a vital save.
54 minWhat a huge goal that could be for the hosts! Samaras drills a low cross into the box and it is cleared only as far as Kayal on the edge of the area. The Israeli opts to side-foot it towards goal inside of going for power, and his shot takes a huge deflection off Denswil which takes it past the keeper. It is desperately unlucky for Ajax, but Celtic aren't complaining.
56 minAjax have responded very well to going two down and are knocking on the door right now. Celtic need to weather this storm otherwise all of their hard work could be undone quickly.
58 minSigthorsson has a glorious chance to pull a goal back within a couple of minutes for the visitors, but he curls his shot wide from close range. His blushes are spared by the linesman's flag, although the replay shows that he was, in fact, onside.
60 minKayal finds a small amount of space from 25 yards out and, having just scored from outside the area, there is only one thought in his mind. He is quickly closed down on this occasion, however, and his shot is tame and easy for the keeper to collect.
62 minUPDATE: Basel have taken a 1-0 lead against Steaua Bucharest, while Atletico Madrid are now 3-0 up against Austria Vienna. Napoli also broke the deadlock in their match at the end of the first half and still lead Marseille 1-0 through Callejon.
64 minPENALTY CLAIM! Lovely football from Ajax as they exchange a number of one-touch passes around the box. It is eventually fizzed in to Sigthorsson, who does well to control it before his strike hits Van Dijk. The visitors want a penalty for handball and it does look like it may have struck the arm of the defender, but he was too close to the ball for it to be given.
66 minDe Jong is trying to take this game by the scruff of the neck now, and he almost does it there. He works space to shoot from 25 yards out and fizzes a low strike towards the bottom corner. It is always moving away from goal, but it has Forster worried enough to be at full stretch as he tries to save it. In the end, it goes a yard or so wide.
67 minKayal is coming into this game more now too. He travels with the ball for a while before letting fly from just outside the box. He also keeps his shot low, but it isn't too troublesome for the Ajax keeper.
68 minAJAX SUB: Christian Poulsen's evening is over as he makes way for Nicolai Boilesen in the first change of the day.
70 minThis is quiet an open game now, and Celtic need to be careful that they don't get carried away with the excited buzz around the stadium. The wisest thing for them to do would be to slow the game down and plug the middle of the field up. Ajax are finding more space in the final third than Neil Lennon will be comfortable with at the moment.
71 minCELTIC SUB: Joe Ledley continues his recovery from injury with another 20 minutes here. He comes on for goalscorer of the second Kayal.
71 minCeltic have caused problems from corners today, and they almost seal the win through that passage. Ambrose rose highest to meet it, but some good defending at the last second ensured that the ball went out for a corner.
73 minAJAX SUB: Another chance for the visitors as Lesly de Sa comes on in place of Fischer. Can he help Ajax launch an unlikely comeback here?
75 minUPDATE: Chelsea and Napoli have both doubled their leads against Schalke and Marseille respectively. Torres got the goal for Chelsea - his second of the day - while Zapata netted for Napoli.
77 minCELTIC SUB: Lennon is not happy here. He initially chose to make the sub before changing his mind as Ajax were awarded a free kick in a very good position. However, the referee ordered the sub to take place, so Lustig makes way for Nir Biton.
79 minUPDATE: Dortmund have taken the lead again at the Emirates! It is Lewandowski who has got the goal this time, making it 2-1 to the Germans in North London.
81 minAJAX SUB: The third and final change of the day for Ajax sees Lasse Schone replace Van Rhijn.
82 minSchone's first action is to stand over a free kick in a promising position. A good delivery would put the keeper under heavy pressure with the defence facing their own goal, but the sub fails to beat the first man. What a waste.
83 minA couple of times in the last few minutes Stokes has made some lung-bursting runs to chase down the Ajax keeper, forcing him into hurried clearances that give Celtic the ball back. It is great desire and commitment shown from the Celtic man at such a late stage.
85 minUPDATE: Porto held out for almost the entire match with 10 men, but finally their resistance has been broken by Zenit, who now lead 1-0.
86 minSAVE! More decent build-up play from Ajax as they patiently wait for the right opportunity to shoot from the edge of the box. Eventually they work the ball back to Blind, whose low strike is fairly comfortable for Forster.
88 minFor once, silence engulfs Celtic Park as the whole ground is shocked by the emergence of a red card. The referee, who has been so lenient and so good all day, is expected to draw a yellow from his pocket at worst, but Biton is as surprised as anyone to see the red card come out. It was a reckless challenge, and his foot was a little high, but that was not a sending off offence. That is the first poor decision the ref has made all night, but it is a big one.
90 minYou can be sure that if his side weren't in such a privileged position here, Lennon would be going mad on the touchline right now.
90 minSAVE! Forster is called into action again, but it is fairly comfortable for him once more. Schone went for goal from range and his effort moved a lot in the air, but Forster would have been very disappointed if he had missed that one.
90 minThere will be four minutes of added time at the end of this match.
90+1 minCELTIC SUB: Lennon responds to that red card with his final change of the night, bringing on Amido Balde for Pukki.
90+3 minCeltic make a hash of clearing a tame cross into the box and De Sa finds himself with time and space in a good position. He completely mis-hits his cross, though, and the ball falls to the feet of Sigthorsson, who is quickly crowded out.
90+4 minAjax get there goal, but it is surely too little too late. It is patient play from the visitors once more as they move the ball around the edge of the area before Schone finally lets fly with a fine powerful strike into the corner. Forster had no chance.
9.41pmCeltic pick up their first points and their first goals of the Champions League group stages with a fairly comfortable 2-1 win over Ajax. They were handed a late scare by Schone goal having been reduced to 10 men controversially, but the visitors left it too late and Neil Lennon's side held on for an invaluable victory.
9.43pmThat result sees Celtic leapfrog Ajax into third place in Group H, two points behind AC Milan, who drew with Barcelona tonight. The Bhoys will travel to the return leg in Amsterdam full of confidence after this result. They didn't let Ajax create much and, although they also struggled to make chances, they probably just about deserved the win.
9.45pmRight, that's all we have time for tonight! Thank you very much for joining Sports Mole for another famous European night in Glasgow as Celtic ran out 2-1 winners over Ajax to move into third in Group H. Be sure to stick around for the match report and reaction, which will be on site shortly, and also to check back in with us for another round of Champions League fixtures tomorrow night. Until then, though, it is goodbye from me!