Ali's hundred was also the second quickest by an England batsman at this level after Jos Buttler's 46-ball ODI century against Pakistan in Dubai in 2015.
Joe Root had earlier made his own bid for top billing when he posted most runs, across all formats, in an English global summer on his way to 84 as he and Ben Stokes (73) first put the hosts on course for a formidable total in their fourth-wicket stand of 132.
Moeen, who hit eight sixes, set a world record by taking only 12 deliveries after passing 50 to bring up his third ODI hundred, helping England to a mammoth 369-9.
"I just had a slog really and everything seemed to come off".
Rain delayed the start of Tuesday's series-opener in Manchester by two hours, with England going on to win a match reduced to 42 overs per side by seven wickets.
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Root and Stokes took over until, for the second time in the innings, two wickets fell in consecutive overs.
In response West Indies were 101/2 in 14 overs with Chris Gayle leading the chase with an unbeaten 61.
A third six from the left-hander took him to a 38-ball half-century, but Plunkett had Shai Hope (20) caught behind and Marlon Samuels (11) went the same way when he was harshly adjudged to have feathered through to Buttler on review.
Earlier, England one-day captain Eoin Morgan's run of low scores continued when he was caught behind for a first-ball nought by a Holder delivery that cut away off the pitch.
By contrast, Test skipper Root is enjoying a run-laden summer.
He eventually holed out off spinner Ashley Nurse and walked off to a standing ovation from a near-capacity crowd.