England had never previously beaten Sweden in a competitive fixture and things were looking ominous in this Kiev clash when Olof Mellberg’s early second-half double cancelled out Andy Carroll’s imperious opener.
However, substitute Walcott’s introduction swung the momentum back in England’s favour as he equalized before creating the winner for Welbeck to leave England in a strong position to progress and Sweden on their way home from Euro 2012.
Scott Parker produced a flying save from Andreas Isaksson on seven minutes after an improvised one-two with Welbeck, but there was nothing the Sweden goalkeeper could do about England’s opener on 23 minutes.
Steven Gerrard directed an angled ball into the box and his Liverpool team-mate Carroll eluded his marker to power home a header from near the penalty spot.
Ashley Young wasted a good chance before half-time but the tables were turned after the break as Sweden struck twice.
After Carroll had given away a needless free-kick, and England had failed to avert the danger, Mellberg eventually saw his shot cross the line despite Glen Johnson’s desperate attempts to clear.
If there was fortune about his first goal, the former Aston Villa defender would not have believed his luck at the space he was afforded on 59 minutes to head home Sebastian Larsson’s free-kick.
Roy Hodgson responded by throwing on Walcott for James Milner and the England coach was rewarded within three minutes when the Arsenal winger lashed home a dipping shot from the edge of the area.
Joe Hart produced a brilliant save from Zlatan Ibrahimovic before Walcott’s pace had Sweden retreating inside their penalty area on 78 minutes and his cross was superbly flicked home by Welbeck.
Captain Gerrard had a late chance to score a fourth, but was denied by an excellent reaction stop from Isaksson as England held on to secure a win which leaves them needing to only avoid defeat against co-hosts Ukraine on Tuesday to ensure qualification for the quarter-finals.
France sit above England at the top of Group D on goal difference after beating Ukraine 2-0 earlier in the day.
Hodgson admitted his disappointment at the two goals England conceded from set-pieces, but accepted such things can happen against sides of Sweden’s quality.
He was impressed with the way his players came back, though, and was keen to savor the victory.
Speaking to BBC Radio 5 Live he said: "It was a cracking game of football. We were reasonably comfortable at half-time and had a good control of the game before they rocked us on our heels.
"We knew how dangerous they were from set-pieces and they proved true to that. But it was very good the way the team responded to that.
"It’s difficult at this level, we’re playing against good teams. Our attacking play showed good intentions and we looked dangerous.
"We limited them to not too many opportunities in free play.
"We got a good victory against a team with good experience and a team that can boast many caps."
Information from The Associated Press was used in this report.