The hosts nullified Australia's attack for most of a captivating final day as they sought an unlikely draw but they eventually surrendered to a 185-run defeat.
England saw off 84.3 of the 98 overs scheduled for Sunday but succumbed at 6.15pm when the dogged Craig Overton was given out lbw after batting 105 balls for his 21.
Overton had shared in a determined ninth-wicket stand with Jack Leach that lasted 64 minutes and cranked up the tension, but their efforts were not quite enough.
Australia's victory gave them a 2-1 lead in the series and meant they would retain the Ashes regardless of the result in the final Test at the Oval.
Australia's Steve Smith was not surprisingly named player of the match after his first-innings 211 and quickfire 82 in the second.
Tweet of the day
Cricket's world governing body appears to be suggesting an England fan's actions in wearing a mask of Steve Smith crying after Australia's ball-tampering fiasco has come back to haunt him in this series.
Quote of the day
The Australia captain praises his team after a tumultuous period stretching back to last year's ball-tampering affair.
Australia's win ensured they would leave England with the Ashes for the first time since 2001. Since then, which at the time was a fourth successive series win in England, Australia have lost in 2005, 2009, 2013 and 2015.
Australia's twin number ones
Steve Smith may have noticeably underlined why he is the world's number one batsman, but team-mate Pat Cummins also showed just why he is currently ranked as the game's top Test bowler. Cummins bowled 48 overs in the match (24 in each innings) and returned match figures of seven for 103 (three for 60 and four for 43).
All not lost for England?
Australia may be celebrating retaining the Ashes but they are not yet guaranteed a series win. Victory for England at the Oval next week would see the series end 2-2 – a feat that in other circumstances would be considered a success.
Overton and Leach frustrate Australia
The stubborn ninth-wicket partnership between Overton and Leach that held up Australia's victory charge lasted 64 minutes and occupied 84 balls. Leach took 54 balls out of the game, scoring 12 runs in the process, while Overton contributed six to the 23-run stand in 34 balls. They also did their best to delay the game, with Leach again needing to clean his glasses and calls for the 12th man to come on.
Australia appear to have picked up on a weakness in Jason Roy's defence, the England batsman having now been bowled four times in the series, more than any other. He was beaten twice through the gate in this game, by Josh Hazlewood and Pat Cummins. He was not the only player unable to defend his stumps, however. Nine of the wickets to fall in the game were bowled.
Crowd did their best
The 23,500 sell-out final-day crowd did their best to roar England on to a famous draw. They tried to break a lot of the tension with chants, thunderclaps, the throwing of cards and continual goading of Nathan Lyon over his costly missed run out at Headingley. They even tried a rain dance. Alas to them it was all to no avail.