The hosts took Australia's three remaining second-innings wickets in 39 minutes of play, to win by an innings and 78 runs, with Ben Stokes taking 6-36.
England's second successive three-day victory over their oldest rivals gives them an unassailable 3-1 lead in the series with one match to play.
The margin of victory is all the more remarkable given, it is only 19 months since England were on the receiving end of a 5-0 thrashing by the Australians down under.
England has now beaten Australia in four consecutive home series - their best sequence since 1896.
Meanwhile, Australia captain Michael Clarke, announced he would be retiring from international cricket at the end of the series.