Led by a century from opener Chris Rogers and a 136-run stand with Shane Watson, the Australians had few problems getting the required 201 runs before tea on the fourth day to seal England's fate at the Melbourne Cricket Ground.
England contributed to their own demise with two confidence-sapping dropped catches by skipper Alastair Cook early in the day to take all the steam out of the dispirited tourists.
England now face the monumental challenge of fighting off an Australian clean sweep of the series in the fifth and final Test, starting in Sydney on Friday.
"I think it's a very special win. A lot of people thought we would come here complacent and not have the same willpower to continue to play the same way as in the first three Tests," Australian captain Michael Clarke told reporters.
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Rogers, 36, was out caught behind for 116 off 155 balls cutting Monty Panesar, with his team some 31 runs short of victory. Rogers ran Mitchell Johnson close for man-of-the-match honours.
It was the best fourth innings run chase in 51 years at the Melbourne Cricket Ground since England's 237 for three in 1962-63.