Just three months after England wrapped up a third successive Ashes series triumph by a similarly dominant 3-0 margin back home, Australia wrested back the tiny urn they last held in August 2009.
Ben Stokes made the Australians sweat through the first session on the fifth and final day of the match with his maiden test hundred - England's first of the series - as the tourists chased their improbable victory target of 504.
Once the 22-year-old lefthander was dismissed for 120 in the third over after lunch to reduce the tourists to 336 for seven, though, Australia quickly ran through the England tail.
Mitchell Johnson, whose fiery spells of pace bowling had turned the first two tests, finished with four for 78 after dismissing James Anderson to end England's innings for 353, sparking wild celebrations from his team mates.
Lefthander Stokes, who made his debut in the second test in Adelaide, showed great concentration and no little courage to help England to their biggest innings score of the series.
England had resumed on 251 for five requiring another 253 runs for an extraordinary victory or more likely needing to bat through the final day to save the test.
The yawning cracks that had opened up on the sunbaked wicket added an extra danger factor for the batsmen, with one Ryan Harris delivery to Stokes jagging off into the slips.
It was Johnson who made the breakthrough when Matt Prior took a swipe at widish delivery and got a nick on it to be caught behind for 26.
Two overs later and Stokes, who had edged his way nervously through the 90s, pulled Johnson to the long-leg for four to reach his hundred, pumping his fist in celebration of an impressive knock.
England made it through to lunch at 332-6 but their task always looked too tough and when Stokes was caught behind off spinner Nathan Lyon the end was in sight.
Australia won the first test in Brisbane by 381 runs and the second in Adelaide by 218 runs and will now be targeting a 5-0 sweep in the final two tests in Melbourne and Sydney.