Victory gave them an unassailable 2-0 lead in the third of the five-match series after the second game was washed out last week.
Joe Root with 84 and Ben Stokes (73) were the other main contributors to an imposing total of 369-9 off 50 overs. They shared a fourth-wicket stand of 132 as Root became the highest scorer in all formats in an English international season.
Then Ali took over, reaching his century off 53 balls, the last of them being his eighth six. Only Jos Buttler, from 46 balls against Pakistan in 2015, has ever got there faster for England.
Ali eventually holed out to long-off for 102 as West Indies' labouring bowlers went for 123 in the final 10 overs.
"The ground isn't that big so it's nice to play on it," he told Sky Sports. "I just tried to slog it as much as I could."
Opener Chris Gayle led the response, at one stage hitting Ali for three consecutive sixes, but he never quite had sufficient support and was run out for 94 going for a quick single.
Ali even took the final catch as the innings ended for 245 in the 40th over, Liam Plunkett finishing with 5-52.
(Reporting by Steve Tongue; Editing by Christian Radnedge)
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