Ravi Bopara (82) and Ian Bell (75) shared a stand of 90 at The Oval as England's batsmen consolidated an effective performance from their bowlers to complete the task with six wickets and more than four overs to spare.
Bell, a revelation since his ODI recall last month, brought up his 50 in 71 balls with his fourth boundary and Bopara was more fluent still on a good batting surface in a chanceless half-century from only 54 deliveries.
The outcome was rarely in the remotest doubt once Australia's innings stalled in the middle overs.
Opener Shane Watson's half-century had hinted at much better than 251 for seven after Michael Clarke won the toss. Watson (66) reached 50 with his eighth 4 at a run a ball, but took another 30 over his last 14 runs, before George Bailey cashed in his lengthy reconnaissance in a career-best 65.
The tourists reached three figures in the 20th over, but there was just one boundary, for the loss of Clarke's wicket, in the next 10 as Graeme Swann, in particular, put the brakes on.
It was the off-spinner, too, who got rid of Watson, unable to do any more than chip a straightforward catch into the wind to deep midwicket as he tried to revive the scoring rate.
James Anderson, nursing a tight groin, was unfit and replaced by Jade Dernbach, who took the new ball alongside Steven Finn. The latter saw off the dangerous David Warner early, mistiming a pull for an easy catch into the leg-side ring.
Watson and Peter Forrest had to start again after a half-hour rain stoppage midway through the 12th over. Broad interrupted any momentum, when he had Forrest deflecting the ball down the leg-side, where a diving Craig Kieswetter took a very good catch.
England's seamers were struggling to control their lines, bowling an extra over of wides in the first 16 as they tried to cramp Watson's off-side strokeplay and kept drifting down leg.
But Bopara's part-time medium-pace immediately brought the bonus of Clarke's wicket, attempting to farm off-side runs but getting an inside-edge behind instead.
Thereafter, Watson and Bailey got stuck as Australia appeared to place their faith in the concept of wickets in hand. Bailey and David Hussey, run out by Finn, did enough in a stand of 78 to just about keep Australia in the game. But Bresnan beat Bailey for the first of two wickets in four balls.
England's reply did not need to be much more than competent.
Alastair Cook was lbw pushing forward to first change Clint McKay, and Trott bowled off an inside-edge as he advanced to Shane Watson.
But Bell made few mistakes. Matthew Wade dropped him on 38, standing up to Watson. But after Warner did likewise at point at the start of Brett Lee's second spell, Bell could add only another five runs before being bowled when he missed a cut at the first delivery from Clarke.
Eoin Morgan was saved by DRS when Clarke – and umpire Richard Illingworth, initially – thought he was gone lbw for a second-ball duck.That moment of controversy passed, England continued seamless progress to a routine and impressive win.