England's six-wicket win handed them a 2-0 lead in the five-match series and a clean sweep will make the hosts the top-ranked nation in all forms of cricket.
The series now moves to Birmingham before matches in Chester-le-Street and Manchester.
Knocks from Shane Watson (66 off 80 balls) and George Bailey (65 off 86 balls) in Australia's 7-251 from 50 overs were unable to paper over the cracks in the batting lineup.
The tourists paid the price for becoming bogged down for the second straight match, suffocated by England's attack with only 40 runs coming between the 20th and 35th over.
In reply, Ravi Bopara (82 from 85 balls) and Ian Bell (75 from 113 balls) ensured the target was reached with 4.2 overs to spare.
Clarke said his side had been badly beaten.
"I think the scoreboard at Lord's (on Friday) probably hid how far away the teams were," Clarke said.
"I think England outplayed us at Lord's, it only said 15 runs but I think they outplayed us at Lord's and they certainly outplayed us here."
The skipper spread the blame.
"We have got areas not only with the bat we need to improve but with the ball as well," he said.
There was controversy in the 34th over of England's chase when TV umpire Aleem Dar overturned an lbw decision on Eoin Morgan (43no from 40 balls) despite there appearing to be little evidence of his hitting the ball.
Umpire Richard Illingworth ruled part-time spinner Michael Clarke trapped the Irishman off the second ball he faced to seemingly reduce England to 4-171.
Morgan called for a review and, after several viewings of hot spot, Dar reversed the decision.
"The information I received was that there was clear evidence that he did hit the ball," Clarke said.
"I don't think it had any influence on the game. We needed to take wickets before that."
Paceman Steve Finn (1-36 off nine overs) led the way for England before spinner Graeme Swann (1-27 off eight overs) and Bopara (1-16 off five overs) tied Australia in knots.
It said plenty about Australia's struggles with Swann that his biggest aggravation of the day was teammate Tim Bresnan's dropping of Bailey on 52.
Peter Forrest (12 off 30 balls) came in for Steve Smith in a testing initiation on English turf.
Mitchell Johnson (0-43 off seven overs) replaced Pat Cummins (side strain) but was typically erratic, combining unplayable deliveries with ordinary fare and costly no balls in his first international in eight months.
Seamer Clint McKay (1-42) bowled well but lacked support with Brett Lee (0-58) still waiting to move clear of Glenn McGrath as the highest one-day wicket-taker for Australia.
David Warner grassed a tough chance when Bell was on 70 that would have edged Lee ahead.