The Worcestershire all-rounder sprinted to his hundred off 53 balls, with nearly half of his runs coming via eight sixes, before he fell for 102.
His century also included seven fours, with the left- hander needing a mere 12 balls for his second fifty.
England's total was their largest in a one-day international against West Indies, surpassing their 328 for seven at Birmingham's Edgbaston ground in 2009, and their fifth-largest in this format overall.
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.
But a partnership of 117 in 76 balls between Ali and Chris Woakes (34) turned the tide.
Joe Root (84) and Ben Stokes (73) had laid the platform for a large total with a fourth-wicket stand of 132 in 20 overs before England, 1-0 up in this five-match series following Thursday's no-result in Nottingham, briefly lost their way.
But, with Ali leading the charge, England scored 123 runs in their last 10 overs after being sent into bat by West Indies captain Jason Holder.
Fellow paceman Holder took two for 81 in 10.
Ali's six-hitting assault really got going as England scored a remarkable 50 runs in two overs -- the 45 and 46th of their innings.
He should have been out for 87 when he smashed a Jerome Taylor full toss to point only for fit again Chris Gayle, back from a hamstring injury, to drop the catch.
Ali went to his century with two sixes in three balls off Cummins -- a pull over deep square leg followed by a soaring drive over long-on.
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.
His latest dismissal meant Middlesex left-hander Morgan had scored just 22 runs in his last nine innings across all domestic and international cricket.
By contrast, Test skipper Root is enjoying a run-laden summer.
He hoisted Cummins for six on his way to a 41-ball fifty also featuring five fours.
During the course of his innings, Root surpassed former England captain Graham Gooch's record of for most runs across all formats in an English international season of 1,277 in 1990 -- although this was his 24th innings compared to the 15 that Gooch had 27 years ago.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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