Australia started Day 3 on 241-7, and the English took the three wickets they needed in 10.2 overs.
England won with two days and more than two sessions to spare, taking an insurmountable 3-1 lead ahead of the final test at The Oval.
England has won five of the last seven Ashes series, and the last four at home.
Mark Wood took the series-clinching wicket when Nathan Lyon played the ball on to his own stumps, sparking wild celebrations among England's players.
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