The Australia captain hit 105 off 102 balls and shared a 155-run partnership with George Bailey (82) for the fourth wicket, making England pay for putting the tourists into bat in the second match of the series. The first ODI at Headingley was washed out on Friday.
Boyd Rankin was the most economical of England's battered bowling attack, with the paceman's 2-49 including the wickets of Clarke and Matthew Wade in successive balls as the run rate slowed late on.
The Australians are looking to make amends for their 3-0 loss in the Ashes test series, part of a dismal tour of England in which they were also knocked out of the 50-over Champions Trophy at the group stage.
Eoin Morgan's decision to insert Australia on an easy-paced surface offering early assistance to England's seamers paid early dividends when Steven Finn enticed a nick from Shaun Marsh on the fourth ball, without a run having been scored. Shane Watson was given out lbw on the next ball but he sought a review and the decision was reversed after HotSpot indicated a slight edge.
Clarke, who said he would have batted if he'd won the toss, laid into England's bowlers with a flurry of boundaries and finished with 14 fours for his first ODI hundred against England and the highest individual score by an Australian at Old Trafford.
Bailey was even more belligerent, his six down the ground off Ben Stokes bringing up his fifty and arguably the shot of the innings. Bailey struck five fours and four sixes in his 67-ball knock.
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