The visitors scored 316 for eight after being sent in to bat in the dead-rubber series, having conceded the first three games. (Agencies)
Emerging star Ben Stokes showed the way with a polished 70 off 84 balls, helped by Jos Buttler's late surge of 71 off 43. Opener Ian Bell kicked off with 55 from 52 deliveries on what looked a prime batting deck.
Under-pressure captain Alastair Cook made a crisp 44 from 43 balls at the top order, only to fall when a much-needed big score seemed likely for the embattled skipper.
Wicketkeeper-batsman Buttler chimed with some scintillating batting in the latter overs to boost an innings that appeared to have lost its way, hitting four sixes as he top-scored.
For just about the first time on the tour, England got on top of paceman Mitchell Johnson, who went wicketless and conceded 72 runs from his 10 overs, although he was on the wrong end of two dropped catches.
The tourists, beaten in all eight of their previous encounters with Australia at Test and limited overs level on a nightmare tour, finally enjoyed some good fortune as the home team couldn't maintain their previous efficiency in the field.
Australia rested three key players for the match -- captain Michael Clarke, wicketkeeper-batsman Brad Haddin and opener David Warner.
Having taken virtually every chance offered by England all summer, the Australians dropped their fielding standards, grassing two chances and also squandering a couple of other opportunities.
At one stage, they missed three chances in two overs.
When Bell was on 48, he cut Nathan Coulter-Nile to deep square and James Pattinson charged in off the boundary, only to have the ball bounce between him and the rope to bring up the Englishman's half-century.
Then local favourite Shaun Marsh, celebrating his recall to the national Test squad for the upcoming tour of South Africa, spilled two catches at first slip in a single Johnson over -- one each from Bell and Stokes.
Australia were also guilty of wayward bowling, conceding 16 wides, with James Faulkner claiming 4-67.
Cook had been quoted as saying he was reconsidering his role as captain leading up to the match, but at the coin toss vowed to do all he could to hang onto the position.
The left-hander finally looked back in form during his knock, hitting three successive boundaries off Nathan Coulter-Nile and playing some sparkling shots either side of the wicket.
However, he was clean bowled by spinner Glenn Maxwell at 44 to continue his frustrating tour.
The visitors scored 316 for eight after being sent in to bat in the dead-rubber series, having conceded the first three games.