England were set a target of 129 to win the fourth Test after bowling out Australia.
The following-on Tourists were out for 387 in their second innings, on the fourth day at Trent Bridge on Sunday.
Victory for either side would see them take a 2-1 lead in the five-match Ashes series with just next month's final Test at The Oval to come.
England last won an Ashes series in 1986-8.
Steve Harmison finished things off with the wickets of Michael Kasprowicz and last man Shaun Tait.
He had earlier won a fortunate lbw decision to remove Simon Katich for 59 and had figures of 3-93.
Michael Clarke (56) and Shane Warne (45) also batted well but no-one played the major innings Australia required.