The tourists came agonisingly close to a 2-0 series lead, which would have ensured Tim Paine became the first touring captain to retain the urn in England since 2001.
Australia, devoid of morale and momentum after Stokes’ unbeaten 135 meant England completed their highest chase in Test history, must instead reset with this week’s tour game in Derby before the five-Test series continues at Old Trafford on Wednesday week.
England, skittled for 67 in their first dig, required 73 runs from Stokes and Jack Leach’s final-wicket stand after a collapse of 5-41 on a topsy-turvy fourth day at Headingley.
Leach scored a single run as Stokes outdid Ian Botham’s 1981 Ashes heroics, hogging strike during a six-hitting rampage that featured a couple of chances.
“I wouldn’t say we were rattled. No doubt there was pressure,” a gutted Paine said.
“It was close, tight. The crowd was loud, that was as hard as it gets for a touring side. Sometimes people make mistakes and we made a couple.
“It cost us the Test match. That and an unbelievable innings.
“We have time now to make sure we stick together, bounce back … we’ve been in a position to win every Test in the series.
“We’re doing something right, we have to keep believing in that.”
The result is a hammer blow to Australia’s confidence given pundits were calling for Joe Root to step down as captain after England’s shambolic collapse on day two.
Since 1888, no team has won a Test after being bowled out for less than 70.
“It’s unbelievable,” Stokes said.
“I have to take it all in. I’m not sure that will ever happen again.”
Nathan Lyon’s final over was Australia’s nadir in the nerve-jangling contest.
A terrible mix-up between Stokes and Leach should have resulted in the latter being run out, but Lyon fumbled at the non-striker’s end when the ball was tossed back to him by Pat Cummins.
Lyon and his 10 teammates went up for a desperate lbw appeal after the next delivery struck Stokes’ pad, but it was turned down by umpire Joel Wilson.
Stokes would have been out on review but Paine wasted his final referral in the preceding over on a far more optimistic lbw shout from Cummins.
Leach clipped a ball off his hips to level the scores then Stokes cracked Cummins’ next ball through the covers to level the series, triggering wild scenes from the delirious allrounder, crowd and dressing room.
“‘It’s going to sting,” Paine said.
England had never hauled in a target higher than 332 to win a Test, while Don Bradman’s 1948 Invincibles had been the only team to chase down more than 342 to win a Test in England.
England had been 17 runs away from victory when Marcus Harris dropped a diving catch in the deep offered by Stokes.
Josh Hazlewood, who snared match figures of 9-115, shifted momentum by snapping Stokes’ 86-run stand with Jonny Bairstow then Travis Head’s composed fielding helped snag two wickets before an epic finish.
Paine said later he had only himself to blame after wasting the review that could have retained the Ashes.
Ball-tracking replays confirmed umpire Wilson erred with the Nathan Lyon lbw shout and the on-field verdict could have been overturned on review.
Ben Stokes disputed that verdict, arguing “DRS has got that completely wrong … cannot believe it was three reds”, but the match-winning allrounder’s opinion would have counted for zero if Paine had the power to send it upstairs.
However, Australia’s skipper had already burned both referrals as his ineffectual use of the system continued to prove a talking point in the series.
Paine insisted Wilson’s verdict, which comes after the Trinidadian’s contentious ruling on a catch as third umpire at Lord’s and some eight overturned decisions in the Edgbaston series opener, was “irrelevant”.
But the keeper struggled to hide his disbelief, noting in a post-match interview with Nine that he “can’t fathom why or how that wasn’t given out”.
“England had two referrals, so if it was given out the correct decision would have been made upstairs,” Paine said.
The veteran then told reporters he “saw it live, that’s all I needed to see”.
“I don’t want to watch that again,” Paine said.
“To sit down and single out an umpire is unnecessary. He is no different to everyone else, he is allowed to make mistakes.
“I’ve got every review wrong, so I’m going to give up and give it to someone else.”
Wilson’s struggles in Birmingham led to calls for English and Australian umpires, who make up more than half of the elite panel, to adjudicate in the Ashes.
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