England, who had led through Andy Carroll's bullet header, conceded twice during a wretched 10-minute period after half-time to leave them deep in trouble.
But manager Roy Hodgson's decision to replace James Milner with Arsenal attacker Walcott had an almost instant reward.
Within four minutes, Walcott collected a cleared corner on the edge of the box and equalised with a 20-yard shot that deceived Swedish goalkeeper Andreas Isaksson.
And 14 minutes later, the England winger burst into the penalty box, went past two Swedish defenders and crossed for Danny Welbeck to flick in the winner.
It was a game-changing contribution from the 23-year-old, who was making his first appearance in a major tournament and scored his first England goal for nearly four years.
England's display in numbers
Theo Walcott was in possession for 15 seconds but was successful with all of his crosses and passes
Walcott's goal was his first for England since scoring a hat-trick against Croatia in a World Cup qualifier on 10 September 2008
Walcott became England's first substitute to score in a European Championship finals match
Ashley Young and Andy Carroll lost possession on the most occasions for England - 18 times each
England have the best conversion rate of any team at Euro 2012, scoring with a quarter of their shots
Joe Hart is only behind Republic of Ireland's Shay Given for the most saves made in Euro 2012
The victory was the first time England have beaten Sweden in a major tournament
Ashley Cole played his 20th match in a major tournament, equalling the most ever by an English player. David Beckham and Peter Shilton also played 20
BBC pundits on Match of the Day
"At 2-1 down you really feared for England. They were disjointed, they gave two bad goals away and there didn't look any way back for them.
"To be fair the spirit was fantastic and when Theo Walcott came on he changed the game. He completely pushed back the Swedish defence, England got more space as a result, they kept the ball better and got two fabulous goals.
"The first goal may have been a bit lucky but the movement, the passing and the ball retention was so much better for the second goal. We wanted them to do that for the whole game, and the important point was they had a bit of penetration at the end.
"It's easy to keep the ball at that point because the opposition is tired and the game is stretched but we need to learn to keep it in the early part of the game."
"You want guys coming on to make an impact, whether that's defensively or offensively, and certainly Walcott did that.
"He gave England pace and energy going forward, because in James Milner and Ashley Young in particular - who I thought was poor - they didn't offer a great deal.
"We are going to need heart in this tournament because we are not good enough at keeping the ball. We did it for the winning goal, but that was the only time in the game when we actually passed it with a little bit of composure."
What others said about England's win:
"I wouldn't say I was the game changer. It's always nice to come off the bench and show what you can do. I've been disappointed that I haven't played." -
"I'm happy with the finish and to get three points but it was disappointing to let in two goals. We came back, we stuck together and the team spirit showed." -
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