The Australian captain scored 105, his eighth ODI hundred, and received strong support from his deputy George Bailey (82 from 67 balls) as the tourists posted 7-315 from their 50 overs after losing the toss.
Needing a record run chase to win, England were bowled out for 227 with wicketkeeper Jos Buttler offering most resistance with 75 from 65 balls.
The result at Old Trafford handed Australia a 1-0 lead in the five-match ODI series after game one in Leeds was washed out.
After a frustrating tour, which has featured a 3-0 Ashes series loss and a winless Champions Trophy campaign, Clarke's side is determined to end a three-month campaign on a high.
And while the skipper refused to get carried away with the win, he said it was nice to finally put a complete performance together.
"It's a good start to the series for us ... but today's only the start," Clarke said of Australia's first ODI win over England in England since July, 2010.
"We've got three more really important games and hopefully we can continue to perform the way we have.
"We won't take anything for granted ... but I think, at the end of the day, it's nice to have won a game against England on this tour."
While Australia's batting proved its weakness in the Test series, the top order has looked strong in the limited-overs format, albeit with England missing the core of its Ashes squad.
England captain Eoin Morgan won the toss and sent the tourists in on a flat wicket, with Clarke claiming he would have chosen to bat anyway.
But Clarke and Bailey were the chief architects of the innings, combining for 155 runs in less than 22 overs.
Clarke brought up his century off 94 balls, raising the bat for his first ODI ton in 18 months on the ground where he scored 187 in the third Ashes Test.
"I seem to score some runs here," Clarke said.
"It was nice to contribute."
Bailey, who hit four sixes, fell short of his second ODI hundred when he was caught by James Tredwell off the bowling of Ravi Bopara (2-57).
Clarke's innings came to an end when he was caught behind from Boyd Rankin (2-49), who then bowled Matthew Wade for a duck the next ball.
The run chase began poorly for the hosts, with Johnson dismissing Michael Carberry and Jonathan Trott within three balls to have the hosts 2-9.
Kevin Pietersen (60) threatened to get England back in the game before presenting James Faulkner with a straight-forward catch off Watson's bowling.
England's slim hopes effectively ended when Morgan (54) was out to McKay, although Buttler ensured the home side went down fighting.
"Today was a bad day," Morgan said.
"We probably let them get 40 too many."
Australian legspinner Fawad Ahmed received some tough treatment, particularly from Pietersen, and finished with 1-55 from seven overs.
The series continues in Birmingham on Wednesday.