Australia had set a challenging target of 316, driven by Clarke's 155-run partnership with George Bailey (82) against below-par bowling from England, who also struggled to get going with the bat and were bowled out for 227.
England, who won the test series 3-0 last month, lost the last two post-Ashes one-day series in 2009 and 2010-11 and a battling 75 from Jos Buttler was the main positive to reflect on as they seek to avoid a repeat with three matches remaining.
The hosts, who rested some of their top Ashes performers, won the toss and chose to bowl on a sunny early morning start after the first one-dayer at Headingley was rained off but did not put up much of a fight as Australia piled on the runs following a bad start.
Opener Shaun Marsh fell for a duck to the fourth delivery of the day and Shane Watson almost went first ball before surviving after a review on an lbw decision.
Watson was not so lucky second time round when England called a review of their own and he was given out for 38.
The Hotspot technology did not show any contact between the bat and Ravi Bopara's delivery, caught by Buttler, but the loud thud that accompanied Watson's swipe was enough to change the umpire's original call.
Opener Aaron Finch made 45 off 45 balls before Joe Root caught him at long on.
Bailey's fine innings, which included five fours and four sixes, ended when he was caught by James Tredwell off Bopara as the skies above Old Trafford darkened.
Clarke found the gaps with ease as he stroked 14 boundaries while notching up 105, his eighth one-day century, from just 102 balls.
England's bowlers finally made an impression when Boyd Rankin took the wickets of Clarke and Matthew Wade (0) with successive deliveries.
James Faulkner was out for 18 in the final over as Australia posted an imposing total of 315 for seven wickets.
The threat of rain at Old Trafford eased but the black clouds gathered for England as their reply began with the early dismissals of opener Michael Carberry (4) and Jonathan Trott (0) after some excellent bowling from fast bowler Mitchell Johnson.
They were then steadied by a 60 from the experienced Kevin Pietersen, selected despite recent knee problems, before he drove Watson's delivery to Faulkner to break up what had been a promising partnership with Eoin Morgan.
Shortly after Australia had claimed the prize wicket of Pietersen, Bopara was caught and bowled by Adam Voges for one to plunge England deeper into trouble on 103 for five.
Captain Morgan brought up his 18th one-day half century to give his side a glimmer of hope but it was snuffed out as he fell for 54 when he sliced Clint McKay to Clarke.
Two more wickets fell quickly with Ben Stokes (5) caught by Bailey off McKay and Tredwell (1) run out and while Buttler fought on to 75, his fifty sealed with a thumping six, he could not prevent the inevitable as the tail fell away following his dismissal.
The third one-day international is at Edgbaston on Wednesday.
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