They showed great heart and courage when Walcott woke them up from a 10-minute meltdown to fight back from 2-1 down and Danny Welbeck's clever finish sealed their first competitive win over the Swedes who were eliminated from the tournament.
"I was very pleased with the performance of the two front players and of course Theo's contribution was enormous today," England coach Roy Hodgson told a news conference.
"To come on as a sub and score such a good goal and set up a winner he's got to be very pleased with his contribution."
The English fans were largely outnumbered in the streets of Kiev and inside the Olympic stadium but they were not silenced at the end of a dramatic game that started 15 minutes late after the France v Ukraine match was suspended for almost an hour.
England are joint top of Group D with France, who outclassed Ukraine 2-0, with the co-hosts in third place on three points and Sweden with none. England will advance if they draw with Ukraine in Donetsk on Tuesday.
Hodgson, in his fourth match in charge, had called on his players to show discipline and commitment against Sweden and they duly delivered, except for a mad 10 minutes when they collapsed defensively and conceded two sloppy goals.
But Walcott, on his first appearance in a major tournament, turned the game around, scoring three minutes after coming on for the ineffective James Milner on the right wing.
Walcott collected the ball just outside the box and calmly fired a fierce shot past Andreas Isaksson before whizzing down the flank to deliver a delightful cross for Danny Welbeck who diverted the ball into the net with a backheel flick 12 minutes from time.
England started well, organised in a clear 4-4-2 with Andy Carroll, brought in to exploit Sweden's weakness in the air, partnering Welbeck up front.
WHIPPED CROSS
The choice paid off when Carroll powerfully headed home from a perfect whipped Steven Gerrard cross midway through the first half.
Sweden were toothless up front with Zlatan Ibrahimovic a pale shadow of his brilliant self but a carbon-copy of the sulky, nonchalant player he can often be.
That counted for nothing early in the second half when the England defence short-circuited, leaving the unmarked Olof Mellberg to bundle the ball in from close range.
Glen Johnson tried to clear on his line but he could only help the ball into the net.
It seemed it was only a matter of time before England conceded another goal and that proved to be the case.
Ten minutes later, Joleon Lescott and John Terry went missing, allowing Mellberg to head home with goalkeeper Joe Hart stranded on his line.
That was when heart and commitment, Hodgson's favourite watchwords, were remembered by his players.
Focused again, they collected the ball much higher up the pitch, earning the corner that led to Walcott's equali
