Following a goalless first half, Erik Hamren's charges went ahead eight minutes after the break when Zlatan Ibrahimovic converted a neat layoff from Kim Kallstrom.
However, Ukraine captain Andriy Shevchenko levelled matters three minutes later with a fine diving header, before grabbing all three points for his side in the 62nd minute when he nodded home a cross from Oleg Gusev.
Here, ESPNSTAR.com takes a look at the players that took to the field in Monday evening's game.
Andriy Pyatov - 6
Spilled a couple of shots but was fortunate the ball didn't end up at the feet of a Swedish player or in the back of the net. Definitely needs to improve especially when Ukraine come up against the other big guns in the group.
Taras Mikhalik - 6.5
Marked his man well and did not allow Ibrahimovic much time and space with the ball, until the crucial moment when the Swedish ace got the opener.
Yevhen Selin - 6.5
The Ukrainians were left fuming when play went on with Selin on the ground, resulting in a goal. Great sacrificial defending on his part though, putting his body on the line to block everything Sweden threw at his side.
Yevhen Khacheridi - 6.5
Khacheridi had an easy task marking Rosenberg and kept things simple at the back. Was always first to any eminent danger and bailed his keeper out of trouble on a few occasions.
Oleg Gusev - 7
The wing-back linked up well with the enthralling Yarmolenko down the right for Ukraine. His fitness levels were just out of this world as he ran up and down the flanks tirelessly.
Serhiy Nazarenko - 6
Couldn't get his passing right and he was the Ukrainian version of Elm. His corners and free-kicks were no better.
Anatoliy Tymoschuk - 7
Great ball distribution from midfield, finding his pacy wingers intelligently. Doubled up as a central defender whenever there were gaping holes at the back, and didn't allow any space for Sweden to exploit.
Evgeni Konoplyanka (92' off) - 8
The highly rated winger who has caught the eyes of Arsenal's Arsene Wenger did not disappoint. Got the crowd to their feet every time he touched the ball as he was fearless down the flanks, taking anyone and everyone on and even managed to grab an assist for Shevchenko's second.
Andriy Yarmolenko - 7
Had one notable shot on goal but it was fired a shot straight into a sea of blue shirts. A bright prospect for the future, Yarmolenko was never afraid to take defenders on and was exciting to watch from start to finish. He even came up with a pinpoint cross for Shevchenko to score the equalizer which injected belief in the boys in yellow.
Andriy Voronin (85' off) - 7
His fierce strike just before the break ensured Isaksson was alert and on his toes. Gave the Swedish defence nightmares with his work rate and his trickery in the final third.
Andriy Shevchenko (81' off) - 9
His team would have been a goal up at the break had he been able to finish like he used to. Blame it on the tight angle perhaps? But no worries, he levelled the scores three minutes after Ibrahimovic scored and doubled his tally six minutes later proving to everyone including his coach that old is indeed gold!
Artem Milevskiy (81' on)
Ruslan Rotan (85' on)
Marko Devic (92' on)
Andreas Isaksson - 6
Did everything he could to keep a clean sheet but clinical finishing from Shevchenko proved too much for his defenders and the Swedes left the pitch emptyhanded as a result.
Olof Mellberg - 6.5
No-nonsense defending from Mellberg, who hacked down every Ukrainian player who threatened his goal. Went forward to make the numbers in the dying minutes in search of an equalizer and was almost rewarded with a goal.
Andreas Granqvist - 6
Denied Yarmolenko with an excellent block in the penalty box but the pace and movement of Ukraine's wide players were too much for him to handle.
Martin Olsson - 6.5
Was tight at the back against Yarmolenko and Gusev, which was no easy feat. Occasionally contributed with some forward runs and good crosses from the left as well.
Mikael Lustig - 5
Struggled to cope with Konoplyanka all game and his stocks fell even further when he was caught dreaming at the near post, allowing Shevchenko to power home a header from a corner.
Kim Kallstrom - 6.5
His only notably contribution to the game was the cut-back for Ibrahimovic to score, which wasn't surprising as the attack-minded Kallstro barely had a sniff of the ball with Ukraine enjoying a lot more possession.
Rasmus Elm - 6
Poor service from him negated Sweden's height advantage. Elm probably should have left the set piece duties to Larsson.
Sebastian Larsson (68' off) - 6.5
Worked hard in the wide areas and did well to whip in balls for Ibrahimovic to work with but like the rest of his team mates, he did not see much of the ball.
Ola Toivonen (66' off) - 5.5
One of the few Swedish players who made full use of his height advantage as he won several headers. However, Toivonen was not as effective with his feet, and failed to reproduce his club form on the international scene.
Markus Rosenberg (71' off) - 6
With only six international goals to his name, Rosenberg desperately needs to prove his worth in the national side and hasn't scored in a Swedish jersey for almost five years. Only had two strikes in a similar position on target all game which were easily kept out.
Zlatan Ibrahimovic - 7
The moment Ukraine's defence switched off, Ibrahimovic clipped the post with a brilliantly-controlled header that left Pyatov rooted to the ground. He didn't have to wait long to find the back of the net as he was left with the simplest of tap-ins soon after the restart.
The AC Milan marksman showed what a star he is by not only putting away chances, but creating them for his team-mates too.
Anders Svensson (66' on) - 5.5
Svensson failed to alter the course of the match as Ukraine were not only a goal up when he entered the fray, but were also enjoying the majority of possession.
Christian Wilhelmsson (68' on) - 5.5
Hamren must have thought Wilhelmsson could provide something extra down then flanks, but all he could do was put in crosses for yellow shirts to clear. Sweden might have been better served with Larsson on the pitch instead.
Johan Elmander (71' on) - 6
Did not look comfortable on the ball after coming back from injury, but he almost was Sweden's hero when he volleyed a ball narrowly over near the end.