Victory saw Australia take a 1-0 lead in the five-match series following Friday's washout in Leeds on the ground where they suffered a 4-0 ODI campaign loss to England last year.
Australia captain Clarke's 105, only his eighth hundred in 229 matches at this level, was the cornerstone of a total of 315 for seven and came after he'd made 187 at Old Trafford in the drawn third Test against England last month.
England, having only twice before made more than 300 to win an ODI, slumped to nine for two as Mitchell Johnson took two wickets in three deliveries and were dismissed for 227 with 34 balls to spare.
"It's nice to get a win and it's a good start to this series for us," said Clarke at the presentation ceremony.
"To make over 300 was a really good score and all our bowlers executed."
Earlier, Ashes-winners England -- resting James Anderson, Stuart Broad and Graeme Swann ahead of the return series 'Down Under' starting in November -- appeared to be at least one bowler 'light'.
However, stand-in England captain Eoin Morgan said: "I don't think we were a bowler short... I'm not concerned by the balance of the side."
Australia seemed set for a total well in excess of 300 but former Ireland paceman Boyd Rankin (two for 49) checked Australia's progress with two wickets in two balls including that of Clarke.
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