Roy Hodgson's men will only need a draw from their final outing with co-hosts Ukraine on Tuesday to claim a last-eight berth. When the dust finally settles, Hodgson will take huge satisfaction from the knowledge both his bold selection moves, picking Andy Carroll and introducing Theo Walcott, paid off handsomely.
Less palatable will be replays of the defending that forced England to launch their memorable fightback after a half-time lead turned into a deficit, with Olof Mellberg twice taking advantage to put Sweden in front.
There was no sign of the drama to come during a drab first half. Scott Parker brought a decent save out of Andreas Isaksson after Welbeck rolled an inviting lay-off into his path. Welbeck guided a header wide from James Milner's cross too.
Sweden had a few half-chances and Sebastian Larsson brought a decent save out of Joe Hart. However, with Zlatan Ibrahimovic enduring one of those evenings when English fans wonder what the fuss is all about, Sweden seemed to be there for the taking.
The opportunity England craved was a while in coming and, as so often, Steven Gerrard provided it. From virtually the identical position he created Joleon Lescott's goal in Donetsk on Monday, the captain launched another inviting cross to the far post.
Carroll got between defenders and rose majestically to power his header into the bottom corner. Much as he may bristle at what is perceived to be the criticism of straight-forward tactics, if England are good at it, Hodgson should make no apology for playing to such strengths.
It is not as though England are incapable of incisive passing when it suits, though. Cole threaded an excellent ball through Sweden's defence for Young to run on to. A poor first touch cost the Manchester United man valuable momentum, though, and he ended up snatching at his shot, which Isaksson saved by the near post.
How galling so much good work was undone within four minutes of the restart. Carroll fouled Kallstrom 30 yards from the England goal, and after that, it was all down to luck.
In lifting the ball back into the box after his initial free-kick had been blocked, Ibrahimovic could not have expected to pick out Mellberg, completely unmarked, eight yards out. Hart made a terrific one-handed save, only for the ball to bounce straight into Glen Johnson, whose desperate attempt to keep it out of the net met with failure.
And, it only got worse for England. Having proved how adept they at scoring from deep crosses, England showed difficulty in defending them as Larsson drove a touchline free-kick deep into the box. Despite so many bodies around him, Mellberg was completely on his own and gave Hart no chance from point blank range.
Hodgson took immediate action, replacing Milner with Walcott. Once again his decision was a master-stroke. Three minutes later, Walcott, hanging back at a Gerrard corner, collected the loose ball from a Sweden clearance, and with defenders and attackers merging in a frenzy of movement to retake their positions, fired through the lot.
Isaksson, unsighted, was totally deceived and could only watch helplessly as the shot flew past him, only a few inches away but completely out of reach. It was Walcott's first goal since that hat-trick in Croatia almost four years ago, and probably his best international performance too.
The goal blitz had squeezed the contest completely out of shape. Even though both sides could still advance with a last-game triumph as things stood, neither were prepared to settle for it. Hart shovelled Ibrahimovic's shot wide before England countered and got their winner.
As Arsenal man Walcott drove toward the byline, he pulled a cross back to the near post, where Welbeck, instinctively, back-heeled it in.
The result leaves Hodgson wondering how to restore star man Wayne Rooney to his starting line-up given Carroll and Welbeck were so impressive. Gerrard was foiled by Isaksson in stoppage time to deny England a more handsome final scoreline.