Leading the series 3-1, at the Gabba Australia’s batsmen paid the price for poor shot selection and the home side blew a good start to struggle to 249 after winning the toss and electing to bat.
The downside for England was an apparent hamstring injury to young paceman Ajmal Shahzad while bowling late in the innings.
Shahzad, a member of England’s World Cup squad, limped off at the end of his eighth over, having pulled up sore four deliveries earlier.
The 21-year-old Woakes, recalled to replace spinner Michael Yardy, rattled the Australians with 6-45, his victims including four of the top six batsmen, among them captain Michael Clarke, who had finally shown some form with the bat.
It was only the second six-wicket haul by an English bowler in ODIs, the other by Paul Collingwood.
Woakes started the rot for the home side when he had dangerous opener Shane Watson caught at point for 16 with the score on 48.
He later removed Clarke (54), Cameron White (16), David Hussey (34), John Hastings (13) and Brett Lee (0) as the home side lost its way.
Clarke showed signs of a long overdue return to form by top-scoring for the Australians, but fell when his team needed him to accelerate the innings in the last 10 overs.
Leading the side in the absence of the injured Ricky Ponting, Clarke was booed by local fans when he came out to bat.
It was the culmination of a poor season where he previously posted just one score over 50 for Australia, having been out of form in Test cricket, ODIs and Twenty20s.
He finally broke the shackles of a dreadful summer when he hit paceman Steve Finn, making his ODI debut, for successive boundaries early in his innings.
However, the loss of Marsh and the underperforming White, after opener Brad Haddin had earlier thrown his wicket away, restrained Clarke and he had to settle for trying to rebuild the Australian innings.
The experiment of promoting Marsh up the order failed for the third match in succession when he fell to Collingwood in the gentle seamer’s first over, while White was removed by Woakes.
When Clarke did decide to take on the bowlers late in the innings, he played a dire shot, advancing down the wicket to Woakes and skying a catch to his English counterpart, Andrew Strauss.
Clarke had faced 74 balls and hit five boundaries.
The all-rounder hammered an unbeaten 104 off 48 balls to secure a five-wicket victory for Australia
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