Chris Rogers scored a sparkling 116 after being dropped on 19 by England captain Alastair Cook, as the hosts mowed through the 201 runs required at the start of play to finish on 233-2 in front of an ecstatic crowd of more than 38,000.
Shane Watson struck a four to bring up the winning runs and finished unbeaten on 85, with Australia captain Michael Clarke on six.
Australia will head to Sydney for the final match of the series, confident of sweeping England 5-0 seven years after Ricky Ponting's team whitewashed the tourists in 2006-07.
Image: Chris Rogers of Australia leaves the field after scoring 116 runs during day four of the fourth Ashes Test
Photograph: Gareth Copley/Getty Images
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