Ali, who arrived with England 210-5 and wobbling at the County Ground, devastated the West Indian bowling with the second fastest ODI century by an Englishman.
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 global season of 1,277 in 1990 - although this was his 24th innings compared to the 15 that Gooch had 27 years ago.
Root and Stokes both went in a rush of three wickets for 11 runs as Cummins briefly interrupted home progress.
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Then Ali took over, reaching his century off 53 balls, the last of them being his eighth six.
England put themselves one more win away from sealing the series, with two matches left to play.
Fellow paceman Holder took two for 81 in 10.
Ali was joined by Chris Woakes with England precariously placed at 217-6 and after a few overs of rebuilding, Ali sprung into life.
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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.
He eventually holed out off spinner Ashley Nurse and walked off to a standing ovation from a near-capacity crowd.
Ali bludgeoned 102 off 57 balls, with seven fours and eight sixes, to get England to 369-9 batting first, its fifth-highest ODI total.
By contrast, Test skipper Root is enjoying a run-laden summer.
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He went to his hundred with successive sixes off Cummins in an incredible burst of scoring which brought him 61 runs from only 13 balls.