Spain booked a Euro 2008 quarter-final spot after David Villa's last-gasp goal sank Sweden and Russia beat Greece.
Spain took the lead on 15 minutes with a clever move that ended with Fernando Torres poking home David Silva's cross.
But Sweden responded well and levelled when Zlatan Ibrahimovic met Fredrick Stoor's cross on 34 minutes.
Spain, who could have had a penalty when Johan Elmander barged Silva, were frustrated by Sweden keeper Andreas Isaksson before Villa's neat finish.
Spain were far less stylish than they had been in despatching Russia in their opening match.
But Villa's goal, his fourth of the tournament, was still enough to put his side into the quarter-finals.
Spain will also top Group D and avoid the in-form Netherlands in the last eight.
As against Russia, they again showed neat touches in the early stages with some quick passing helping them to outmanoeuvre the hard-working Swedes.
But Lars Lagerback's side were not as easy to break down and it took a move of real ingenuity to put Spain ahead.
A quickly taken Xavi corner resulted in the ball being fed short along the bye-line to Villa and, from his quick pass, Silva whipped the ball in to Torres who stretched to prod it home at the near post.
Sweden had created nothing up to that point yet they should really have been level seconds later.
Henrik Larsson cleverly shielded the ball on the edge of the Spanish area before playing in Elmander but he shot wastefully into the side netting.
Spain were still having all the possession but they were struggling to make it count and it was Lagerback's more direct approach that began paying dividends.
Ibrahimovic's lobbed pass put Larsson clear but, although the veteran striker had to wait for the ball to come down in the area, he will still be disappointed with his eventual shot, which he spooned high over the bar.
While Sweden were pumping balls into the area they remained dangerous, however, and it was through that method that they equalised.
Spain were undoubtedly missing Carles Puyol, who had limped off injured, when Stoor fired in a cross from the right and Ibrahimovic had time to take the ball down and slot home.
The big striker's first touch was poor but he easily shook off a weak challenge from Sergio Ramos and although Iker Casillas got a hand to his shot, he could not keep it out.
Spain had gone quiet by this point but they still should have had a penalty just before the break.
Zlatan Ibrahimovic finds space to score Sweden's equaliser
Silva was preparing to meet a Ramos cross from the right when he was blatantly pushed over by Elmander but referee Pieter Vink chose to ignore the challenge.
Sweden could be pleased with their work in the first 45 minutes and it appeared they were happy with a point, taking off Ibrahimovic to save his troublesome knee, and sitting deep as the second period began.
Their reluctance to come forward frustrated Spain, who had used the counter-attack to such lethal effect against Russia.
Cesc Fabregas came off the bench to help create some openings but Spain found Isaksson in solid form when they did get within shooting range.
The Manchester City keeper spilled a low Silva shot but recovered to keep out Villa's follow-up before Torres' shot was blocked by Daniel Andersson.
Isaksson made another smart stop to keep out Marcos Senna's stinging effort on the run soon after and it looked as though Sweden had done enough for a draw.
But Villa had other ideas, latching on to Joan Capdevila's pass in the 92nd minute and expertly sliding the ball into the corner of the net.
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Sweden: Isaksson, Stoor, Mellberg, Hansson, Nilsson, Elmander (Sebastian Larsson 79), Andersson, Svensson, Ljungberg, Henrik Larsson (Kallstrom 87), Ibrahimovic (Rosenberg 46).
Subs Not Used: Shaaban, Wiland, Linderoth, Alexandersson, Majstorovic, Granqvist, Allback, Wilhelmsson, Dorsin.
Booked: Svensson.
Goals: Ibrahimovic 34.
Spain: Casillas, Sergio Ramos, Marchena, Puyol (Albiol 24), Capdevila, Iniesta (Santi Cazorla 59), Senna, Xavi (Fabregas 58), Silva, Villa, Torres.
Subs Not Used: Palop, Reina, Fernando Navarro, Alonso, Sergio Garcia, Guiza, Arbeloa, Juanito, De la Red.
Booked: Marchena.
Goals: Torres 15, Villa 90.
Att: 30,000
Ref: Pieter Vink (Holland).
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man of the match: Spain's Fernando Torres 7.93 (on 90 minutes).
Russia 2-0 Sweden: Thousands of Swedes descend on the Tivoli Neu stadium in Innsbruck for the vital clash against Russia
Swedish defender Mikael Nilsson is pressurised by Russia's Alexander Anyukov as the crucial encounter gets under way
Russian pressure results in a deserved lead as Roman Pavluchenko fires home from Aleksandr Anyukov's pass in the 24th minute
Andrei Arshavin slots home a superb second for the Russians after latching on to Yuri Zhirkov's cross from the left in the 50th minute
Arshavin's goal is just reward for a fine personal and team performance as Russia head for a quarter-final clash with Holland
