Roy Hodgson's preferred methods are orderly but a chaotic, crazy evening was a landmark occasion for England and their new manager.
Their Swedish jinx was ended, a first competitive win under Hodgson secured and their Scandinavian rivals eliminated in a game of two comebacks.
The first came from the Swedes, Olof Mellberg turning a one-goal deficit into a 2-1 lead.
The second was inspired by Theo Walcott, who scored the equaliser and fashioned Danny Welbeck's winner.
England join France on four points at the summit of Group D and know that a draw against Ukraine on Monday would propel them into the quarter-finals. For Hodgson, the manager who only took over in May, that would amount to success.
It was an evening when, despite the anarchic feel, much the England manager did worked. His introduction of Walcott turned trauma into triumph while the initial selection of Andy Carroll was also justified.
With Carroll's inclusion, England began in more positive mood and more direct manner. They had been working on crosses in training, looking to exploit Sweden's strange fallibility - they are a tall team - against the aerial ball. Practice paid a dividend.
Having supplied Joleon Lescott's goal against France with a free kick in a similar position, Steven Gerrard showed his supply line is just as effective in open play. His curling cross was met by Carroll with a thumping header.
England's aerial threat was already apparent. Danny Welbeck had glanced a header wide after James Milner crossed. The closest they had come, however, was with a stinging shot from Scott Parker that Andreas Isaksson repelled.
Ashley Young had been moved to the left in the reshuffle to accommodate Carroll and had a chance to double the lead, dragging his shot into the side-netting after a first-time pass from Ashley Cole. At that stage, England were in control, with Carroll tormenting the Swedish defence and Gerrard dominating the midfield.
It was a match where both captains made an impact, however. There is an inevitability to Sweden's threat revolving around Zlatan Ibrahimovic. The talisman tested Joe Hart with one drilled effort and was thwarted by Glen Johnson, with a fine recovery challenge, on another occasion.
Yet Ibrahimovic's role in the equaliser was unorthodox, to say the least. After Carroll conceded a free kick, his strike rebounded off the England wall. The Swedish captain scissor-kicked it back into the box where the lurking Mellberg shot. Neither Hart, who got a hand to it, or Johnson, who made a desperate attempt to clear on the line, could prevent it from trickling in.
That goal was debited to Johnson. There was no denying that Sweden's second belonged to Mellberg, however. He was utterly unmarked when Sebastian Larsson swung in a free kick and the 34 year old planted his header past Hart.
At that stage, England were on the brink. Defeat would not have guaranteed their exit, but it would have rendered it very likely. Hodgson reacted. The limited Milner went off, the lithe Walcott game on.
The fightback started. First Isaksson made a superb save to deny John Terry. Then Walcott's deflected shot flew past the Swedish goalkeeper.
And the Arsenal winger's catalytic cameo was completed when he sped down the right and crossed and Welbeck finished delicately and delightfully, flicking the ball in. Job done, though not in the manner Hodgson envisaged.
France beat Ukraine, s6