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England, who resumed on 18-2, were bowled out for 197 on the final day, with Australia seamer Pat Cummins taking four for 43.
Australia's victory, with 81 balls remaining, was a convincing one but England's spirit cannot be criticised as they fought until the final hour in their attempt to save the test and keep the series alive.
The tourists lead 2-1 going into next week's final test at The Oval where they hope to become the first Australian team to win an Ashes series in England since 2001.
Steve Smith, whose magnificent double century and then second innings 82 were the key factors in this win and whose batting throughout the series has ensured the Ashes remain in Australian hands, was delighted.
"It feels amazing to know the urn is coming home. I've been here a few times when things haven't gone our way. This was always one to tick off my bucket list. It's extremely satisfying," he said.
The main early resistance from England came from Joe Denly who made 53 from 123 balls and Jos Buttler, who lasted 111 balls for his 34.
England’s hopes of an unlikely escape-act rose when Jack Leach and Craig Overton batted for over an hour giving the crowd belief over a second 'miracle' after the comeback win at Headingley.
But part-time leg spinner Marnus Labuschagne finally removed Leach, with a ball that turned sharply in the rough and was gloved to Matthew Wade at short leg.
Overton batted with sense, stoicism and a strong technique, but he was trapped lbw by Josh Hazlewood to set off the Australian celebrations.
"I didn't think it would be this emotional," Australia captain Tim Paine said.
"The amount of work that's gone in to retain the Ashes has been enormous and I'm really proud of this group and how we bounced back from Headingley," he added.
England captain Joe Root told the BBC: "I'm bitterly disappointed. I thought the way we fought today, the character we showed, every single one of them can be proud of that today.
"To come so close to taking it to The Oval is hard to take. We've still got to look forward and make sure we level the series."
England will look back on the second day of this test as the turning point when they simply could find no way to remove Smith and Australia's 497-8 declared gave them an advantage that they were unable to seriously challenge.
The final day was never going to be a run-chase of Headingley vintage, given the target of 383, with England's task simply to survive until the close.
That challenge was made all the more difficult after they lost Jason Roy and Ben Stokes before lunch.
Roy was well set before the impressive Cummins bowled him for 31 with a beautiful delivery that cut back off the seam to leave England at 66-3.
The crowd rose to welcome Stokes, the hero of England's last day triumph at Headingley, but there was to be no repeat performance from the all-rounder.
Another fine delivery from Cummins clipped the inside edge of Stokes's bat and was well taken by wicketkeeper Paine, the England batsman not waiting for the umpire's verdict as he walked off.
Denly had been the pick of England's batsmen before he was outdone by sharp turn and bounce from spinner Nathan Lyon, the ball striking his glove and being snaffled up by Labuschagne at short leg.
Jonny Bairstow (25) was lbw to Mitchell Starc before Overton came in to join Buttler, in what was probably England's last realistic chance of a big partnership.
But Buttler misjudged a delivery from Hazlewood which he left only to see it cut back sharply and clatter into his off-stump.
Australia keep the Ashes, which they won on home turf last year and it is the first time they have retained the urn since the end of their long period of domination in 2002.
There is though plenty left to play for when the teams meet again at The Oval on Thursday -- England could level the series while Australia will be desperate to ensure they go home as winners.