Adelaide: England were bowled out on the fourth ball of the last over as the hosts fought back from what had looked like a losing position for most of the match.
James Faulkner. Pic/ AFP
The visitors had restricted Australia to 217 for nine wickets with a tight bowling display, but themselves ended up all out for 212.
Skipper Michael Clarke praised Australia's spirited fightback.
"A magnificent performance by the boys, with the ball especially," he said.
"I thought our batting was disappointing today," Clarke admitted. "For us to win the game, we had to bowl England out."
And they did just that in dramatic fashion with England needing just six runs to win.
The visitors contrived to turn another winning position into defeat.
"We should have got over the line there. We got ourselves into a good position," said captain Alistair Cook.
"Credit to Australia: in the end they held their nerve better than we did. Poor shots were played under pressure."
Cook flies home on Monday after a miserable tour which included a 5-0 Test whitewash.
"Australia have had a great summer against us and they have managed to win the critical times," he said.
"It has been a tough couple of months for us but, you know, we've got a lot of things we can work on."
"In 12 months' time we should be in better shape for the World Cup," in Australia and New Zealand next February and March.
Both sides found batting difficult on a day when the bowlers were well on top on a slow drop-in pitch.
George Bailey top-scored for Australia with 56 off 74 balls, while Joe Root hit 55 for England but took 86 balls to do it.
Root fell flicking an attempted ramp shot straight to Xavier Doherty at short fine leg off James Faulkner at a time when England seemed to be cantering to victory.
Danger man Eoin Morgan had just gone for 39 off 40 balls after he struck the first six of the game.
He had looked the only really comfortable batsman on either side until he smacked Faulkner straight to Shane Watson at mid-off.
Root just needed to stay at the crease but fell in a moment of madness. Wickets then tumbled rapidly and the required rate soared to a run a ball.
England were unlucky at the death to lose Ravi Bopara to a ball that bounced off wicket-keeper Matt Wade and just removed the bails as the batsman's foot lifted off the ground.
The stumping decision was a long time coming. But when Bopara walked off after scoring 25, England were in deep trouble on 209 for nine.
Tail-ender Chris Jordan could not connect for a boundary and James Tredwell clipped Watson to the keeper with two balls remaining.
Nathan Coulter-Nile finished with figures of three for 34 runs off his 10 overs and Clint McKay, who did much of the final damage, took three for 36.
For England, paceman Stuart Broad had led the charge, snaring three key wickets for 31 runs off his 10 overs including two maidens.
England wrap up the tour with three T20 matches starting in Hobart on Wednesday, Melbourne on Friday and Sydney next Sunday