Denmark dominated the first half of the second leg tie, but were unable to break their opponents down, as Ibrahimovic gave Sweden the lead from a corner on 19 minutes with one of his side's few opportunities.
The 34-year-old added a second after the break with a well-struck free kick, before Denmark netted twice to give hope to the Copenhagen crowd, but Morten Olsen's side had left it too late to complete a comeback.
Relive the action as Denmark and Sweden drew 2-2 on the night with Sports Mole's full text commentary below.
7.15pmGood evening folks! Welcome to Sports Mole's live text commentary of this evening's crucial all-Scandinavian Euro 2016 qualification playoff between Denmark and Sweden. After Saturday's first leg, the visitors hold a slim 2-1 lead, but a late Nicolai Jorgensen goal in that fixture has given the Danes a good chance of overcoming their opponents this evening thanks to the away goal rule.
7.17pmThe team news is out, so let's take a look at how the two sides will line up in Copenhagen tonight.
7.30pmTonight is as big as they come as far as European Championship qualifiers are concerned. More than just a playoff and a local derby, tonight could end the international career of one of two iconic figures in Scandinavian football. Denmark coach Morten Olsson has signalled his intention to step down from the job at the end of his side's Euro 2016 campaign, while Sweden striker Zlatan Ibrahimovic will also do the same. Failure to qualify for the tournament - at the hands of local rivals - is not the way to bow out.
7.34pmHoping not to finish the job tonight, Olsen has made four changes from the side that was defeated in the first leg at the weekend. Yussuf Poulsen, Pierre Hojbjerg and Thomas Delaney come into the starting XI - as does Nicolai Jorgensen, whose late goal on Saturday has given his nation plenty of hope going into this evening's game.
7.39pmThe neutral may prefer to see this man at next year's tournament though. Zlatan Ibrahimovic has scored 60 goals in 110 international appearances for Sweden - nine in nine for 2015 - and an away goal from the Paris Saint-Germain striker could end this tie as a contest this evening.
7.41pmA quick look at the history books suggests that Sweden may have the advantage, having won 46 previous encounters to Denmark's 40, while 18 clashes have been drawn. History and form can both go out of the window on nights like this though.
7.43pmPREDICTION! The national anthems have been sung, and there are less than five minutes to go until kickoff, so it's time for a prediction. I think Denmark will edge it tonight 1-0. Home advantage and an away goal will be enough to push Olsen's side over the line for me, but it will be a nervy affair. It could be a different story if Zlatan performs at his very best though.
7.44pmA minute's silence has just been observed following the devastating attacks in Paris on Friday evening, and kickoff is about to get underway.
2 minIbrahimovic is getting a fair bit of unwelcome noise from the home crowd this evening! Sunderland's Larsson slips a pass in front of the big man, but it is asking far too much of the veteran and goes out of play.
3 minFirst set piece of the evening goes to the hosts, as Durmisi wins a corner off Lustig.
5 minNothing comes of the delivery though, and Sweden clear their lines eventually. Delaney then tries to play in Jorgensen for Denmark, but Isaksson is first to the ball.
7 minA half-chance for Denmark as Pierre Hojbjerg whips a decent cross towards Yussuf Poulsen, but the forward can't quite connect to the cross with a header. Immediately after, Berg leads an attack for Sweden, which Denmark intercept for a throw. A good start to the game from both sides this evening, with a real derby intensity.
9 minCHANCE! Huge moment for Denmark! Lars Jacobsen wins a corner, and from Christian Eriksen's delivery Poulsen flicks towards goal. Lustig tries to intercept the ball, but touches it onto the crossbar - very nearly an own goal! Agger's follow-up attempt was blocked, before Delaney fired over the bar.
11 minYELLOW CARD!Pierre Bengtsson picks up a booking for a cynical challenge on Yussuf Poulsen. Durmisi takes the resulting free kick, but his effort goes over the bar. The Danes have made a terrific start to the match - they just need a goal.
14 minCHANCE! Jacobsen plays in Poulsen on the right, before the forward dribbles past a few Sweden defenders before firing a tame effort at Andreas Isaksson. The hosts are getting closer.
16 minEriksen wins a free kick as Lewicki pulls the Tottenham Hotspur man, who was advancing towards the box in graceful fashion. Durmisi takes it short to Eriksen, who shoots from distance, but hits the wall.
19 minGOAL! Denmark 0-1 Sweden (Zlatan Ibrahimovic)
19 minWell it was against the run of play, but that man Zlatan can deliver at any moment. It was Sweden's first corner as Jacobsen headed behind a long ball from the visitors. Kim Kallstrom took the set piece, which fell to Ibrahimovic on the half-volley, and the big man found the bottom corner of the net.
21 minPerhaps undeservedly so, it's advantage Sweden in Copenhagen. The Danish away goal is now null and void, and two goals are needed just for extra time.
22 minDenmark win a corner, and Andreas Isaksson is forced to punch away the delivery for a throw. The hosts come forward again, but Poulsen is deemed offside and the move breaks down. This game is not over yet.
25 minSweden are just starting to look a little more comfortable with their goal. The visitors knock the ball around for the first time in the game, before playing in Bengtsson on the left, but the full-back's cross is woeful and lands somewhere between Row Z and Finland.
28 minCHANCE! Brilliant save from Leicester City's Kasper Schmeichel! Marcus Berg plays Ibrahimovic in to the left of the penalty area, and you expected the net to bulge, but Schmeichel makes himself big and denies the striker.
30 minFormer Wigan Athletic man Andreas Granqvist gives away a free kick in a very good position for Denmark. Christian Eriksen takes the delivery, and the effort is curving towards the bottom corner, but Isaksson punches behind for a corner - which is headed harmlessly over the bar by a Danish attacker.
33 minSecond corner of the night for Sweden, won by Lustig, but this time Kallstrom's delivery is hacked away and Denmark break, only for the move to break down.
35 minDenmark are probing and probing but cannot make a breakthrough. Bendtner tries a simple cross, but it goes beyond everyone and out for a goal kick.
37 minDurmisi plays an awful pass back to Schmeichel, and the keeper is forced to concede a corner. Kallstrom's delivery finds the head of Ibrahimovic at the back post, but Schmeichel collects the ball from the striker's weak effort. To be fair to Zlatan, there was little else he could have done with the flight of the ball.
40 minCHANCE! A very lucky escape this for Daniel Agger. Sebastien Larsson hoofs the ball forwards, and Ibrahimovic chases, before whipping the ball towards the box. Agger intercepts, but his connection almost sends the ball into the net. Eventually the ball lands on top of the net, and the corner that follows comes to nothing - all to the relief of the former Liverpool man.
43 minIbrahimovic wins the ball in the middle of the pitch and plays in Larsson, who advances before trying his luck, but the effort is blocked.
44 minCHANCE! Decent chance for Nicklas Bendtner, who tries to connect to a whipped cross from Hojbjerg with a header, but the former Arsenal mis-times his effort and Sweden escape unscathed.
45+1 minThe impressive Thomas Delaney plays in Poulsen, but the forward takes an extra touch and is forced wide, before Sweden can clear their lines. One minute of added time to be played.
8.32pmSweden lead 1-0, 3-1 on aggregate, in Copenhagen thanks to Zlatan Ibrahimovic's 61st international goal. For all Denmark's possession and intensity they have been unable to find a way through, and with Ibra in the opposition, Morten Olsen's side have been punished. 45 minutes to save Denmark's Euro 2016 hopes.
8.34pmIf you joined our commentary a bit late this evening, you can read how the first 45 minutes unfolded with Sports Mole's half-time report here.
8.36pmStats time. Denmark have had 64% possession to Sweden's 36%, and 12 shots on goal compared to their opponent's three. Zlatan is the difference this evening, and the PSG striker punished the Danes for their poor set piece defending, and for their inability to hit the target.
8.39pmThis was the moment that Sweden celebrated moving a step closer to Euro 2016.
8.43pmUPDATE: In tonight's other Euro 2016 qualification playoff, Slovenia have a 1-0 half-time lead over Ukraine, meaning that clash stands at 1-2 on aggregate - with no away goals scored and everything to play for. You can read Sports Mole's half-time report on that clash here. But be quick - the second half will be here shortly!
46 minRESTART! Sweden get the second half underway.
46 minSUBTITUTION!Michael Krohn-Dehli comes on for Denmark, not a surprise, but Thomas Delaney is the man to come off, which is.
47 minChristian Eriksen whips in a free kick with pace from the left, but Poulsen is unable to reach the delivery.
50 minIt's been a scrappy opening to the second half in Copenhagen, with Denmark unable to keep the ball, and Sweden happy to watch their opponents struggle. There is still time for the Danes to come back in this, but they need to improve quickly.
52 minDaniel Agger hacks away a Marcus Berg header that troubled the Denmark defence. The hosts break, and Nicolai Jorgensen whips a cross in from the left, which Johansson struggles to deal with, putting it behind for a corner. The set piece falls to the feet of Hojbjerg, but the Bayern Munich youngster cannot keep his effort down.
55 minThe second half has been poor so far, which suits Sweden far more than it does Denmark. Plenty of head tennis and loose passing.
57 minDenmark win another free kick, and it's taken quickly. Michael Krohn-Dehli comes forward with a shot, but Andreas Granqvist places himself in front of the effort. Still Denmark can't find a way through, and it is beginning to look like Sweden's night.
60 minSUBSTITUTION!Nicklas Bendtner comes off - to the delight of the home crowd - and Morten Rasmussen replaces him. Bendtner has been in poor form for Denmark in recent times, and has not done anything to cheer the Copenhagen crowd up tonight.
62 minDenmark win a corner, and Eriksen's delivery is headed behind by Ibrahimovic. Another corner, same taker, same man back defending - and the big striker clears his lines.
65 minDenmark have around half an hour to save their Euro 2016 hopes, but Morten Olsen's team have rarely troubled the Swedish goal in this half. Durmisi drills a ball across the face of goal, but Sweden clear the danger fairly comfortably, a similar story all evening.
68 minA long Daniel Agger throw causes some concern in the Sweden box, but Denmark cannot find a connection and Sweden clear again.
70 minYELLOW CARD! Martin Atkinsson puts Sebastien Larsson into the book for a challenge on Riza Durmisi, which was the Sunderland man's umpteenth foul of the evening.
72 minCHANCE! Somehow Denmark still have not scored. Another long Agger throw causes problems, with the ball falling for Christian Eriksen. The Spurs man looks certain to score, but is denied by Isaksson, before Larsson hacks the ball away.
74 minAll Denmark now, but they need to come up with something. Time is running out in Copenhagen. Durmisi puts in another cross from the left that is far too easy for Sweden to clear.
75 minAgger shoves Emil Forsberg in front of his own box and Sweden have a free kick in a dangerous position. This would kill the tie, and the Swedes have some dangerous set piece specialists...
76 minGOAL! Denmark 0-2 Sweden (Zlatan Ibrahimovic)
77 minWhat did I say? Ibrahimovic bends it around the Danish wall and into the top corner of the net. Game over, and Agger has hacked down Zlatan for another free kick slightly further out. Will it be three?
78 minJust wide from Ibra. What a player he has been for Sweden.
80 minCHANCE! Ibrahimovic turns provider, whipping a ball in from the left towards Markus Berg, but his effort flies over the bar.
80 minSUBSTITUTION! Seb Larsson limps off for Sweden, with Oscar Hiljemark coming on in place of the Sunderland man.
83 minOut of nowhere, a goal for the hosts, but it's surely far too late for a comeback? Riza Durmisi - who has continually put in poor cross after poor cross from left-back - whips in a ball to the far post, where Poulsen heads in. Game on?
84 minFor the record, Denmark need to score two more goals to edge into Euro 2016. An impossible task? Maybe.
84 minSUBSTITUTION! Odd one this... Durmisi - who just chalked up an assist - has been replaced by towering centre-back Jannik Vestergaard.
86 minMorten Rasmussen goes down under the challenge of Andreas Granqvist in the box - no penalty given by Martin Atkinson. For me, a good call, but the Copenhagen crowd certainly don't agree!
87 minIbrahimovic leads a quick break, and plays in Hiljemark on the right, but Denmark intercept the attack.
90 minNicolai Jorgensen wins another Danish corner. Not long left.
90+1 minGOAL! Denmark 2-2 Sweden (Jannik Vestergaard)
90+1 minForget what I said about Vestergaard! The big man - playing as an auxiliary striker - wins a corner off Granqvist, before netting from the second delivery. If only there was more time, but we've played half of the three added minutes.
90+2 minCHANCE! Huge chance to at least win this match for Pierre Hojbjerg! The midfielder plays a one-two before firing from the centre of the Swedish box, only to see his effort sail wide. Should have done better.
9.35pmFull time, and what a game! Two Zlatan Ibrahimovic strikes have seen Sweden qualify for next summer's European Championships. Despair for Denmark, who were the better team for large parts of the night, but were punished by the one of the best players in the world. Strikes from Yussuf Poulsen and Jannik Vestergaard gave Denmark hope, but they left it far too late for a comeback. Morten Olsen may well be stepping down from the Denmark job after this, but we will be seeing this man in the summer.