Brisbane - Australia were chasing 170 runs to win the first Ashes Test after skittling England for 195 off 71.4 overs on the fourth day at the Gabba on Sunday.
The tourists lost six wickets for 82 and faced an uphill struggle once their top batsman and skipper Joe Root was out for 51 in the over before lunch.
Josh Hazlewood trapped Root leg before wicket to the jubilation of the Australians over the significant wicket.
Hazlewood, who removed Alastair Cook and James Vince late on Saturday's third day, finished with three for 46 off 16 overs.
Off-spinner Nathan Lyon started the ball rolling for the Australians on day four when he had Mark Stoneman (27) and Dawid Malan (4), both caught by Steve Smith at slip.
Lyon also removed Moeen Ali with a contentious stumping by wicketkeeper Tim Paine for 40 after the TV umpire needed repeated replays before deciding that the Englishman's back foot was not behind the crease line.
Lyon finished with three for 67 and now has taken 274 wickets in 70 Tests, the highest number of wickets by an Australian off-spinner.
Mitchell Starc chipped in with the wickets of Jonny Bairstow (42), Chris Woakes (17) and Stuart Broad (2) to finish with three for 51.
The third paceman Pat Cummins finished off the England innings when he had Jake Ball caught behind the wicket off a vicious short ball for one.
Australia have a formidable record at Brisbane's intimidating 'Gabbatoir', where they have not lost a Test match since falling to Viv Richards' West Indies in 1988.