Moeen Ali hit 48 from 25 balls and he and Jos Buttler put together a perfectly-timed and unbroken partnership of 77 from 48 balls to lift England from well behind the required run rate to just ahead when rain fell at the Oval and ended play.
England finished on 258-5 in 35.1 overs thanks to the late impetus provided by Ali and Buttler. That was good enough to win by six runs on the Duckworth-Lewis method after West Indies had posted 356-5 from 50 overs.
Buttler was 43 not out from 35 balls alongside Ali, and their match-winning stand put England 3-0 up with one game to play in the series.
West Indies lost despite their best batting performance of the series, with opener Evin Lewis producing a brilliant 176 from 130 balls before he had to leave on a stretcher, retiring hurt, after hitting the ball into his own ankle and sustaining a hairline fracture.
The victory completed a successful summer of cricket at home for England, which won test and one-day series over both South Africa and West Indies, and a Twenty20 series over the South Africans.
That success should have put England in buoyant mood ahead of the Ashes in Australia starting in two months' time, only for the arrest of allrounder Stokes over a late-night incident this week to cast a shadow over preparations.
Stokes, England's test vice-captain and star player in all formats, missed Wednesday's game after his arrest in the early hours of Monday morning on suspicion of causing actual bodily harm in an altercation with another man, reportedly at a nightclub.
Stokes was released without charge but is still under police investigation for the incident that followed England's win in the third ODI. Opener Alex Hales, who was with Stokes on the night out, also missed Wednesday's game at the Oval after returning to Bristol to help police with their investigation.
England's bowling attack felt Stokes' absence as West Indies posted its big total, powered by Lewis and captain Jason Holder (77 off 62 balls).
An unbalanced England attack couldn't keep West Indies under control despite making a strong start.
Chris Woakes took 3-71 and West Indies was 33-3 after 6.1 overs with those early strikes. But a 117-run stand between Lewis and Jason Mohammed (46) and a partnership of 168 off just 108 balls between Lewis and Holder saw West Indies race away. That Lewis-Holder stand was West Indies' best for the fifth wicket in ODIs.
Lewis, who was brilliant with his 17 fours and seven sixes, made the fourth highest score by a West Indian in a one-day game. He was closing in on becoming the first man to make 200 in an ODI in England when he was undone, not by a bowler, but by himself.
He mishit a delivery from Jake Ball into his own ankle and, grimacing in pain, slumped to his knees. He was taken off on a stretcher with just over three overs to go in the innings.
Ali and Buttler came together with England 181-5. Jason Roy made 84 to lay the platform for England but Alzarri Joseph's five wickets had the West Indians in control, and England trailing well behind the required rate.
Ali and Buttler turned that around in the space of just eight overs, with Ali smacking six fours and two sixes and ensuring England will have a victorious end to its summer despite the absence of Stokes.
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