They needed 359 to win, more than they have ever chased in a fourth innings history. With just one wicket left, they still required 73.
History was against them, as well as the maths. The last time any team had won a Test match after being bowled out for 70 had been 131 years previously.
But England had Ben Stokes. It is a wonder Australia ever thought they had a chance.
It might have been fair to assume the summer of Stokes had peaked when he dragged England across the line by an imperceptible margin to win their first 50-over World Cup title at Lord’s in July.
But then he went and trumped it, by scoring a scarcely believable 135 not out at Headingley to keep England alive in the Ashes.
Many are acclaiming it as the greatest Test innings ever played. Shane Warne just called him "Superman".
Once England were all out for 67 after their second day implosion in this third Ashes Test, they were basically cooked.
And, yet, Ben Stokes. The sort of cricketer who equates what everyone else would consider to be impossible odds to be more or less evens. At worst.
For 329 minutes and 219 balls, he defied arguably the world’s best pace attack to win an unwinnable match.
Off the first 70 balls of his innings, he had three. It was exactly the sort of vigilance that was needed at the time.
Then he bookended his effort, amid unbearable tension, by scoring 74 off 45 balls in the last-wicket stand with Jack Leach,.
To bring the score required to less than 50, with just No 11 Leach left for company, he hit one of the most extraordinary shots ever seen in Ashes cricket. A switch-hit off Nathan Lyon for six into the Western Terrace, a stand that was on the verge of a meltdown due to the excess of adoration for Stokes.
For much of Sunday afternoon, they were singing: “Shoes off, if you love Ben Stokes!” Presumably they were all walking home barefoot one the game was done. Either that, or floating home.
It is difficult to write a Stokes eulogy without falling back on words like “Bristol”, “nightclub” or “Brathwaite”, even though his redemption tale was completed ages ago, many times over.
But the Stokes story never does run smooth, even when it scales heights like this latest one. Even within this heroic Greatest Ever Test Innings, there were tough times.
Most notably when he appeared culpable in the run out of Jos Buttler, the man with whom he scripted the World Cup final win (or tie, looked at another way).
Fine alliances with Joe Root and Jonny Bairstow had come and gone, and the impossible dream seemed to hang on the partnership between Stokes and Buttler.
But it was aborted after just eight runs, when Stokes opted against a quick single to Travis Head, and Buttler failed to recover his ground in time.
Whether that aberration affected Stokes is unclear. He could scarcely have been more focused on the task in hand, as it was.
To evidence the point, Stokes celebrated neither his half-century, nor when he reached his ton. There was still a job to do.
Could Australia have stopped him? They really should have. Twice, with two runs left to get, they had the opportunity.
First, Leach was turned back from a nervous attempted single, only for Lyon to drop the ball with the run out at his mercy.
Off the very next ball, Stokes survived an lbw appeal that Hawkeye suggested would have hit the stumps.
Australia had burned their final review in desperation the previous over, off a ball from Cummins to Leach that had pitched outside the batsman’s leg-stump.
Leach scampered a single off the third ball of the next over, from Cummins, leaving the stage open for Stokes to complete his mission impossible with a belligerent forcing shot through cover.