Andrei Shevchenko enhanced his iconic standing as a Ukrainian national hero as he sparked scenes of national celebration with a match-winning double in Kiev.
The home fans were thrilled when their all-time leading goalscorer was somewhat surprisingly included in Oleg Blokhin's starting line-up.
And their joy at seeing their hero in action escalated to delirium as the striker scored twice in the second half to give his side a win in their opening game.
Zlatan Ibrahimovic had fired the Swedes in front, but Shevchenko levelled within three minutes and quickly added a second to send the co-hosts to the top of Group D.
Earlier, group favorites France and England had shared a 1-1 draw in Donetsk.
Defender Joleon Lescott headed England into a first-half lead, but his Manchester City team-mate Samir Nasri levelled for France before half-time.
France 1-1 England
Samir Nasri rescued a point for France in Donetsk after his Manchester City team-mate Joleon Lescott had fired England into a first-half lead.
Lescott became the first Manchester City player to score in a European Championships finals when he headed home Steven Gerrard's free-kick on 30 minutes.
But having waited 52 years for one goal, City quickly supplied another as Nasri dragged France level again. Florent Malouda's searching run allowed Franck Ribery to tee-up Nasri for a clinical strike from the edge of the penalty area that flew past his City team-mate, Joe Hart, six minutes before half-time.
The draw extends France's unbeaten international run to 22 games, while England remain unbeaten after three games under new coach Roy Hodgson.
Hodgson sprung a surprise by including Arsenal winger Alex Oxlade-Chamberlain in his starting line-up, the 18-year-old winning only his third cap.
The youngster and his England side settled well and Hodgson's side should have been in front when James Milner went past goalkeeper Hugo Lloris but fired into the side netting with the goal wide open.
But when Manchester City man Milner was fouled by France's Manchester United defender Patrice Evra, Lescott exacted swift punishment by heading home Gerrard's free-kick from close range.
The lead only last nine minutes, though, as France his back with a well-worked goal that finished when Nasri fired a low right-foot shot beyond Hart's reach.
Ukraine 2-1 Sweden
Ukraine's talismanic striker, Andrei Shevchenko, lit up Group D with a second-half double to defeat Sweden.
The co-hosts' record goalscorer was their hero once again as he took his tally of international goals to 48. But none of the previous 46 will have been more important than this golden double in the Olympic Stadium.
After a lack-lustre first-half Sweden's own striking icon, Zlatan Ibrahimovic, brought the game to life when he turned home Kim Kallstrom's pass to put Sweden in front.
But the goal sparked a response from Ukraine, who struck twice within 10 minutes to turn the game around.
Andriy Yarmolenko was the supplier on both occasions, first cutting back to whip in a left-foot cross that saw Shevchenko react quickest to head home an equalizer.
Six minutes later, Yarmolenko floated a left-foot corner to the near post where Shevchenko escaped Ibrahimovic's marking to glance home a header and put the co-hosts in front.
Shevchenko left to a huge ovation when he was substituted 10 minutes from time, but the Ukrainian celebrations were nearly silenced in stoppage time.
First, Johan Elmander fired over the crossbar after combining brilliantly with Ibrahimovic, then defender Olof Mellberg shinned over the bar with just seconds remaining.