After easing into his day's work with a run-a-ball 39, Moeen let rip in the final six overs of England's innings, crashing eight sixes and two fours in 14 deliveries, to rampage to his third ODI hundred and the fastest ever made on English soil.
Ali started tentatively and his first boundary came after facing his first 15 balls.
England leads the five-match series 1-0, winning the first game before the second was abandoned because of rain.
Jos Buttler holds the record for the fastest ODI hundred for England.More news: Suspected Earthquake detected in North Korea
Veteran West Indies opener Chris Gayle marked his return to the side with a valiant 94 before he was run out by Adil Rashid's direct hit from midwicket after the Jamaica left-hander missed the rainswept no-result at Trent Bridge on Thursday with a hamstring injury.
"I enjoyed myself", Ali told Sky Sports.
England lost three wickets for 11 runs to be 217 for six in the 35th over.
He should have been out for 87 when he smashed a Jerome Taylor full toss to point only for Gayle to drop the catch at point.
All-rounder put on a show in Bristol on Sunday, blasting a 53-ball hundred to get England up to a very big total of 369-9 after half-centuries from Joe Root (84) and Ben Stokes (73). "You try and hold your shape as long as you can and when it's there you have a good go and just keep going".More news: 1 dead, 7 injured after gunman opens fire at Tennessee church
With Ali leading the charge, England scored 123 runs in their last 10 overs after being sent into bat.
He eventually holed out off spinner Ashley Nurse and walked off to a standing ovation from a near-capacity crowd.
In comparison the 48th over was quiet until Ali climbed into a short delivery from Cummins and pulled it over deep square leg to move into the nineties.
Performance of England has been quite mesmerizing throughout the series of cricket matches played against WI. Bristol is not a happy hunting ground for West Indies; they are yet to register a win in three matches.More news: UN Security Council concerned over planned referendum in Kurdistan Region
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