The visitors took a surprise lead with just three minutes on the clock courtesy of a screamer from debutante Darren Maatsen.
However, a Stokes tap-in following a corner ensured that it was all square at the break.
Celtic dominated the match and were only kept at bay by the good form of visiting goalkeeper Mark Brown, but even he was helpless to stop Stokes rifling home a winner in the 87th minute.
Find out how all the action unfolded with our minute-by-minute text commentary below.
4.45pmGood afternoon and welcome to our live coverage of the Scottish Premier League content between Celtic and Ross County. Neil Lennon's side may have coasted to the title last season, but they face a tough test today against a side who are no pushovers.
4.47pmThe new SPL officially got under way last night as newly-promoted Partick Thistle and Dundee United drew 0-0 in an eventful clash that had everything besides a goal. You can read our report on that one here.
4.49pmThere are a couple of other SPL fixtures in play right now. Inverness Caledonian Thistle are 3-0 up against St Mirren, and Aberdeen lead Kilmarnock 2-1. Celtic's bitter rivals Rangers are tied at 1-1 with Forfar Athletic in the Scottish League Cup after trailing for most of the game.
4.51pmBack here at Celtic Park, we have some team news for you...
4.59pmThis may be Celtic's first domestic fixture of the new campaign, but they've already played three competitive matches this season due to their European commitments. They saw off Irish minnows Cliftonville 5-0 over two legs, and currently lead Swedish outfit Elfsborg 1-0 on aggregate.
5.02pmRoss County will prove to be a tough test for the Scottish champions. They were something of a surprise package last term, challenging for European football in their first season back in the top flight.
5.03pmPre-match quotes from both camps coming up...
5.05pmCELTIC BOSS NEIL LENNON: "We have some footage of Ross County and prepared the team for that and I am looking for a good home performance from us rather than worrying too much from Ross County and what they´re going they to do."
5.06pmROSS COUNTY MIDFIELDER GRAHAM CAREY: "Hopefully this season we can do better than [last season] because that should be the bare minimum, especially with the way the club has progressed over the last few years, with the infrastructure, the training ground and the players they've brought in. The minimum requirement is to finish in the top six - less than that will be a failure I think."
5.09pmJust over five minute to go until kickoff, so now seems as good a time as any to offer my prediction. I think Celtic will edge this given their home advantage, but Ross County won't make it easy for them. I'm going for 2-0 to the hosts.
5.11pmCeltic are parading the Scottish Premier League trophy ahead of kickoff. They are the red hot favourites to reclaim it with Rangers languishing in the second division these days, and their journey towards that goal begins right here.
5.14pmYou'll Never Walk Alone never fails to inspire when it rings out across a packed Celtic Park. Kickoff is just moments away now.
0 minKICKOFF: Ross County get us under way at Celtic Park, kicking from right to left. They immediately play the ball long into the Celtic half, but the Hoops win the ball and surge forward.
2 minA let-off for Celtic as Ambrose makes a mistake at the back, allowing Luckassen and Carey in on goal, but the defender back-peddles and recovers well.
4 minMy word! Celtic are left gobsmacked as Ross County débutante Maatsen gives the vistors the lead with a stunning strike from the edge of the box. he was given far too much space there, but the finish was top drawer, going in off the underside of the bar.
6 minIt's been a sloppy start from Celtic, but they just put their opponents under some pressure. Izaguirre surged along the left flank and floated a measured cross into the box. Unfortunately there was nobody there to capitalise on it, though.
9 minRoss County venturing into the final third again as Luckassen chases down a through ball, but he concedes a free kick with a foul on Mulgrew. Boerrigter heads wide from Forrest's cross at the other end moments later.
11 minIzaguirre plays a searching ball into the box that is easily claimed by Ross County keeper Brown. There were a few green and white shirts in the box there, but the goalie was always the favourite to reach it fist.
13 minMore possession from Celtic in the final third as Stokes attempts to line up Commons for a shot inside the area, but his strike partner is closed down and the Ross County defence scrambles the ball away.
15 minWasteful play from Stokes! He regains possession inside the Ross County area and should have shot first time. He had plenty of space but opted to take a touch, eventually giving the ball away.
17 minGreat determination from Kettlewell. He takes on the Celtic backline wide on the left, causing them all sorts of problems. He didn't give up until the ball was far beyond his reach.
19 minCeltic are really dominating possession now, as we expected they would, but they still trail to that Maatsen thunderbolt. They haven't created too much of note in front of goal, but are on the attack now...
20 minCHANCE! Great vision from Commons to pick out Boerrigter on the left. He bears down on goal, but Brown gets his body in the way of it, deflecting it behind for a corner. A good save from the Ross County stopper.
22 minBoerrigter has another attempt at goal, although this one never looked like going in. He hit it straight at Brown from outside the area. James Forrest hits a low drive wide of the right post moments later.
24 minCommons plays a cross into the box from wide on the right. It finds the head of Boerrigter, but it was too long for the Dutchman, bobbling off him and bouncing out for a goalkick.
26 minRoss County look content to defend deep at the moment. They haven't had a single attempt on goal since taking the lead. Commons has just had an attempt turned behind by Brown.
28 minCeltic are level thanks to a poachers goal from Stokes. The ball fell to Lustig following a corner and he stabbed at it, causing it to roll beyond Brown along the line, and Stokes was there to tap home. Not the prettiest goal you will ever see, but the home fans aren't complaining.
31 minThat Celtic equaliser had been coming for some time, but they surely won't be content with 1-1. Expect the heavy bombardment on the Ross County goal to continue.
33 minCHANCE! A neat team move almost yields a second goal for the Hoops. Commons finds Stokes in the area, and he plays it across the face of goal to Boerrigter, but he fails to connect with the pass under pressure from Kovacevic.
34 minBoerrigter injured himself going for that ball from Stokes, and it looks like he's going to have to come off. He is over on the sidelines for treatment...
36 minLooks like Boerrigter is going to attempt to continue. There were fears his afternoon was over there. We can only assume Lennon will be assessing the situation at half time.
39 minSUBSTITUTION: I spoke too soon about Boerrigter. He has been replaced by Tony Watt, whose first contribution is to take on two defenders in the Ross County area and give away the ball.
41 minSHOT! Good defending from Munro prevents Celtic from carving out a goalscoring opportunity, but he concedes a corner. The resultant corner falls to Ambrose in front of goal, but he blazes his shot over the bar.
43 minCommons, Stokes and Forrest link up as Celtic stage another attack. The latter's cross from over on the right drops into the arms of a grateful Brown. The hosts are really dictating the pace of the match now.
44 minSAVE! Ledley picks out Stokes with a lofted pass and he goes clean through on goal. Forester denies him with a good stop as he drills in a effort from a tight angle. Another good save from him.
6.02pmAll square at the break in Celtic's season opener. The Hoops dominated possession, but fell behind to a screamer from Darren Maatsen. Anthony Stokes scrambled home an equaliser in the 28th minute, and it's been one-way traffic ever since.
6.06pmThe visitors have defended well under constant pressure, and Brown has impressed between their sticks, but they look like they will cave if their opponents keep up this bombardment.
6.10pmThere were two matches in the SPL earlier on. Aberdeen edged out Kilmarnock 2-1 and Inverness Caledonian Thistle put three past St Mirren without reply. You can read our reports on those here and here.
6.13pmElsewhere, Celtic's rivals Rangers were knocked out of the Scottish League Cup following a 2-1 defeat to Forfar Athletic. Gavin Swankie struck an extra-time winner in that game to dump more misery on the Gers.
45 minKICKOFF: Celtic get the match back under way.
47 minCeltic on the offensive again as Stokes plays a dangerous pass across the face of goal. Kovacevic puts it behind for a corner under pressure from Watt. Commons takes the corner, but it is hacked clear.
49 minCHANCE! Terrific effort from Stokes. A cross comes in from Forrest from wide on the right and the Celtic striker takes it on the volley, catching it cleanly, but it sails just wide of the post.
52 minOFF THE BAR! Tony Watt squares a pass to Commons in the area. He hits it first time and it comes crashing back off the crossbar! Poor marking from Ross County to allow him to get that shot in.
54 minJoe Ledley bears down on goal with a penetrating run, but he is closed down and dispossessed for a corner. Commons takes it, but his cross is too long for Forrest to get his head to.
56 minCHANCE! Brown plays in a cross from the left and Stokes nods it down for Commons to hit. Micic gets his body in the way to produce a vital block and prevent Celtic from taking a 2-1 lead. Brilliant defending!
57 minSHOT! Ross County venture into the final third. They win a free kick in a good position after Quinn in brought down. Carey curles one over the wall, and it goes over by mere inches.
61 minStokes races along the left flank and fires a low cross into the danger zone. Munro plays the ball back to Brown, but comes dangerously close to putting through his own goal. A let-off for the visitors there!
62 minSUBSTITUTION: Alex Cooper replaces Ross County's goalscorer Darren Maatsen. He made quite the impression in his first game for the visitors.
65 minOFF THE WOODWORK! Commons finds the head of Mulgrew with a looping corner, and his effort comes back off the post. Unlucky!
68 minSUBSTITUTION: Matthews replaces Lustig for Celtic as they search for a winner in this season opener.
70 minSHOT! Stokes has a pop from outside the area after receiving the ball from Izaguirre. Brown makes a comfortable save and does well to hold onto the strike.
72 minSUBSTITUTION: Carey is replaced by Saunders for Ross County with less than 20 minutes remaining. A draw would be a fantastic result for them. Not many teams can say they have gone to Celtic Park on the opening day of the season and come away with something.
75 minRoss County win a corner as Quinn's free kick goes behind off Ambrose. The ball finds its way back to him from the corner and he has a go from outside the box, blocked by Mulgrew. Commons miskicks in front of goal from Watt's layoff moments later.
77 minPENALTY TURNED DOWN! Boos ring out around Celtic Park as McLean brings down Stokes in the area. Celtic appeal for a penalty but the referee isn't interested. Neil Lennon looks furious over on the touchline. It looked 50/50 to me, as McLean appeared to lean into the striker while going for the ball.
81 minCeltic win yet another corner. Forest attempts to play its short to Izaguirre, but Brown gets there first. The goalkeeper blocks a point-blank-range effort from Commons moments later. If Ross County earn a point here today, they will have him to thank.
83 minSUBSTITUTION: Mustafi replaces Luckassen for the visitors with seven minutes remaining at Celtic Park. Ross County are closing in on a good point here.
85 minCeltic have claims 70% of the possession today, a statistic which tells the whole story really. It's Maatsen's goal that will dominate the headlines, but Brown has been superb in the Ross County goal.
88 minA superb strike from Stokes might just have sealed all three points for Celtic. His first goal was a tap in, but this one was anything but. Commons picked him out in the area, and he gave his marker the slip and beat Brown at his near post with a low effort.
90 minSUBSTITUTION: Celtic have brought on Kayal for Forest as they look to see this job through. There will be three minutes of stoppage time for them to play through.
90+1 minThree points is nothing short of what Celtic deserve. They started in sloppy fashion, but have been utterly dominant since they got up and running. Ross County have defended well, but offered little in front of goal.
7.07pmThe Scottish champions get the new campaign off to a winning start thanks to a double from Anthony Stokes. Mark Brown in the Ross County goal played a blinder, but it wasn't enough to keep the Hoops out.
7.10pmThat's all from me tonight. Many thanks for joining Sports Mole for this Scottish Premier League fixture.