After winning the first leg 1-0, Celtic were aware that a clean sheet in Scandinavia would see them move a tie away from the group stages.
They came under pressure during a frantic opening 20 minutes, but after Joe Ledley missing a guilt-edge chance later in the half, they equaled the efforts of their opponents.
The second half saw both sides work hard to create a clear opportunity on goal, and as Elfsborg tired, Celtic ended the match in control to safely progress through to Friday's draw.
Read below to see how the action unfolded in the Boras Arena.
5.46pmHello, and welcome to Sports Mole's coverage of the Champions League third qualifying round fixture between Elfsborg and Celtic.
5.48pmAfter last year's heroics took them to the last 16 of the Champions League, Celtic will be eager to repeat that feat this season. However, they must come through safely against Elfsborg this evening if they are to keep their dream alive.
5.50pmThe team news for Celtic is already in from the Boras Arena in Sweden, so that information is coming up shortly...
6.05pmELFSBORG SUBSTITUTES: Hassan, Larsson, Soderberg, Jorgensen, Claesson, Hedlund, Elm
6.08pmAs you can see from the Elfsborg lineup, striker Mo Bangura has been selected to face his parent club for the second time in a week. His participation had been in doubt after picking up an injury in training, but he has recovered sufficiently to start against the Bhoys. Celtic supporters will be hoping that he doesn't contribute to their demise in this competition...
6.13pmIt should be noted that Bangura hasn't scored in 16 appearances for Celtic, so it would be somewhat of a double whammy should he score against them this evening!
6.16pmElfsborg are currently midway through their domestic campaign in Sweden, currently occupying sixth position with 12 matches remaining. To put things into context, Malmo, who were thrashed by Swansea City last Thursday, are second in the same division.
6.20pmDespite coming out on top at Celtic Park last Wednesday, the Scottish Premiership outfit had probably been expecting to have a healthier advantage going into tonight's game. However, it's one of those fixtures where you think that if Celtic can net that all-important away goal, then they will be as good as through to the final qualifying round.
6.24pmAn extra factor that Celtic will have to contend with tonight is that the game is being played on an artificial surface, which is likely to favour the Swedes. Celtic did, however, record a victory over Spartak Moscow in Russia last season on a similar pitch so they do have some experience on the faster outfield.
6.27pmWe are just over 15 minutes away from the start of the action in Sweden. Who do you have coming out on top?
6.31pmPREDICTION! The first leg indicated that Elfsborg can be more of a match for Celtic than originally anticipated, but with them being forced to place more focus on attack this evening, that could free up space at the back for Celtic to take advantage of and net the away goal that should put this tie to bed.
6.35pmIt's worth noting that Celtic are a game better-off, fitness-wise, since the first leg. Neil Lennon has spoken about his side not being at peak fitness levels just yet, but Saturday's 2-1 victory over Ross County in the Scottish Premiership should benefit them going into tonight.
6.38pmLennon has also stressed that it's not ideal to have such an important period for the club so early in the season, but his side have been used to this scenario for many years, so I'm sure that won't hinder their performance.
6.40pmThe teams are about to emerge from the tunnel at the Boras Arena.
6.45pmFor those unaware, Elfsborg have an Englishman playing in attack, by the name of James Keene. The 27-year-old began his career at Portsmouth, while he also featured for Pompey last season. The referee has just gotten us underway.
2 minElfsborg have had the better of the opening exchanges, but a couple of long balls have just been too strong for Bangura.
4 minIt has been a crisp start from the Swedes. They are moving the ball around sharply, and pressuring Celtic as soon as they lose the ball.
6 minCHANCE! What an effort from Bangura. The ball comes into the Sierra Leone striker, who chests the ball on the edge of the area before sending an overhead kick marginally wide of the post.
9 minCeltic are struggling to make any headway in Elfsborg's attacking third. The Swedes have started at a frenetic pace, and after forcing the Scottish side back, they win a free-kick on the right touchline.
10 minBangura is fortunate to avoid a yellow card after attempting a Maradona-esque handball finish from the free-kick, but the referee opts to just have a word with the forward.
12 minCHANCE! Much better from Celtic. Lustig is sent hurtling down the right wing, before crossing for the awaiting Samaras. However, the Greek striker could only head the ball over from 12 yards out.
15 minCeltic are all over the place at the back. There's poor communication between Forster and a defender, and the ball goes out for a corner, with the Bhoys needing three attempts to get the ball clear. The home crowd have rightly been encouraged by the fast tempo that their team have created.
18 minCeltic have eased the flow of balls entering their final third of the pitch, but Elfsborg are still well on top. They surely can't keep this pace up for the 90 minutes...
20 minFree-kick for Celtic 25 yards out, and very much in a shooting position. It looks as though Commons will step up...
21 minCHANCE! What an opportunity! The free-kick from Commons broke through to Ledley on the penalty spot, but despite being under no pressure, the Welshman fired the ball straight at the goalkeeper. That would have been the tie right there, maybe.
24 minLennon knows how big that opportunity was. All Ledley had to do is find a corner and Celtic would have been 1-0 up. Still, it has been better from the Scottish outfit in the past five minutes.
28 minCeltic are still playing the ball around nicely, but they have stopped making any inroads in Elfsborg's half of the pitch. The Swedes respond with a direct ball into the box, which Bangura heads over from 10 yards. Decent chance.
31 minDespite that chance, Elfsborg have definitely slowed a touch, gifting Celtic more time on the ball. Brown has just been crudely brought down 35 yards out, which has lead to a corner.
33 minSuch a poor corner from Mulgrew though, with the ball curling straight out on the far side. Here comes an early substitution for the home side, with Mobaeck coming off to be replaced by Soderberg.
36 minJames Keene, who I spoke about just before kickoff, has remained on the periphery of proceedings, and he has just attempted to get into the game with a speculative effort from 30 yards, but his shot went harmlessly into the stands.
39 minWell Keene is very much in the action now. He has just picked up a knock after a challenge from Ambrose, but after 30 seconds or so on the deck, he is back up without the need of any treatment.
43 minCeltic are just trying to get through to half-time, but each time they back off, Elfsborg oblige by taking advantage of the extra space, so they need to be careful for the final couple of minutes.
7.32pmLedley went extremely close with a long-range drive with the last kick of the half, but we are goalless at the break.
7.35pmThat wasn't the most convincing of 45 minutes from Celtic, but after weathering the early storm, they will be delighted to have got to half-time without conceding.
7.40pmI don't think Neil Lennon will decide to make any alterations to his side just yet, but if they fall behind, I'm sure the introduction of Anthony Stokes will follow. Samaras has looked solid enough, but he looks slightly short of match fitness.
7.42pmAs for Elfsborg, they are more than holding their own against their stronger opponents. All eyes have been on the performance of Bangura, but while he has looked sharp for the most part, he doesn't look the most orthodox of strikers in and around the penalty area. He was unlucky with his early bicycle kick, though.
7.46pmThe two teams are beginning to make their way back out into the Boras Arena. It doesn't appear as though there has been any changes.
48 minIt's been a fast start by both sides, with both goalkeepers having to be alert to claim the ball after it was played into the penalty area.
51 minSHOT! Elfsborg opt for a clever corner routine, with the ball being played to Larsson 30 yards out, but his first time shot drifted just wide of the post.
54 minCeltic's defending is becoming slightly panicky. They are just trying to clear the ball anywhere, and when they do, it is coming straight back at them. They are lucky to survive a game of pinball in their penalty area, before the referee awards them a free-kick.
59 minCeltic have restored a bit of calm over the past couple of minutes through Brown and Ledley in the middle of the park, but Elfsborg are waiting to pounce should they lose the ball. This is an important period for the Bhoys.
61 minHave Celtic got lucky there? Wilson clashed with Keene in the box, which saw the Elfsborg striker go down, but the referee remained unmoved, despite loud appeals from the Swedish side. It was certainly a strong challenge from Wilson...
65 minIt's all getting a bit sloppy out there now. Both sides are struggling to create any significant chances. Lennon remains unmoved on the Celtic bench. I would have thought he might be thinking about changing things up.
67 minMulgrew plays a final ball directly to Samaras, who lays the ball into the path of Commons, but the hero from the first leg drags his left-foot shot well wide of the right-hand post.
69 minI didn't realise that Stokes had been warming up, but apparently, he had, and he is coming on to replace Samaras. Bold move by Lennon.
72 minIt looks as though Lennon is going to be forced into another change. Mulgrew is down and the stretcher is being brought on. It looks like an ankle injury, with the Scot dragging his foot awkwardly when challenging for a high ball.
74 minAdam Matthews is the man coming on to replace Mulgew, while Elfsborg are also going to make a change, bringing on Hedlund for Hauger.
77 minLess than 15 minutes remaining in Sweden. The game isn't exactly littered with chances, but you wouldn't be surprised if either side nicks a goal, and one that could ultimately decide the outcome of this tie.
80 minCeltic are doing nothing untoward regarding wasting any time, but the referee is jumping on top of any suggestion of it, sometimes a bit too eagerly. Elfsborg earn another corner, but Celtic manage to see off the danger. 10 minutes remaining.
85 minThe atmosphere is not what you would expect for a tie so close. You could hear a pin drop in the Boras Arena. Commons breaks down the right to earn a free-kick for his side, but Celtic make a complete mess of it.
87 minCeltic are making the kind of errors on the ball that you wouldn't expect, but I think the pitch is continuing to play its part. They lose possession once again, but an Elfsborg cross drifts over everyone and out for a goal kick.
88 minBOOKING! Stokes has been throwing his arms about a little aggressively since his introduction, and the referee has had enough and booked the striker. He can have no complaints. He redeems himself by earning his side a corner.
90 minThere will be four minutes of injury time, which is probably about right. Anxious times for the Celtic supporters!
90+2 minCHANCE! Keene does superbly to control a high ball and turn the defender, but his volley was abysmal, and high into the stands. Up the other end, Stokes can only find the defender with two teammates waiting in the box.
90+4 minBangura clashes with Brown, and it causes a few of the Elfsborg players to react to defend their player. But it doesn't matter...CELTIC ARE THROUGH!
8.39pmWell it wasn't pretty, but Celtic have managed to fight through to the final qualifying round of the Champions League. They were far from their best, but they can be proud of keeping their fourth successive clean sheet in Europe this season.
8.41pmFor all their toil in attack, Elfsborg rarely tested Forster in the Celtic goal. If they were clinical in front of goal, the outcome of this tie could have different. At least Celtic won't regret seeing Bangura in the opposition lineup!
8.43pmThat's all from Sports Mole for this match. Celtic don't have to wait long to see who they will play in the final qualifying round, with the draw coming up on Friday. Thanks for joining us this evening. Goodbye for now.