Moeen's 53-ball century - with his second fifty coming off just 12 balls - was the cornerstone of England's imposing 369 for nine.
Moeen Ali's third one-day global hundred and Liam Plunkett's best ODI bowling swept the hosts to the win.
As if the pre-arranged distraction of England's Ashes squad announcement wasn't enough to be taking in, there was also the fall-out from Ben Stokes' antics in Bristol in the early hours of Monday morning.
Plunkett was only hit for six once by West Indies swashbuckling batsman Chris Gayle as he finished with the figures of five for 52 which took him second, only behind Rashid Khan with 33 to the Afghanistan leg-spinner's 36, in this year's table of top ODI wicket-takers.
Instead Moeen Ali (48 off 25 balls) and Jos Buttler (43 off 35) put on a match-winning unbeaten sixth-wicket partnership of 77 in eight overs to ensure that England were just ahead on the Duckworth-Lewis-Stern method when the heavens opened.
Evin Lewis made a stunning 176 before having to retire hurt in freaky fashion during the fourth one-day worldwide against England at The Oval on Wednesday.
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But the latest National Hurricane Center (NHC) advisory warned that Americans have not seen the back of Maria just yet. There is also a storm surge watch from Cape Lookout to Duck including the sound side of the Outer banks.
Moeen Ali's blazing century set up England's 124-run victory over the West Indies in the third One-Day International here as the hosts went 2-0 up with two to play in a five-match series.
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 mishit a delivery from Jake Ball into his own ankle and, grimacing in pain, slumped to his knees.
Jason Mohammed came to the crease and a period of consolidation was broken, when Gayle hit Ali's uncomplicated off-spin for three successive sixes in the 23rd over.
Demonstrating extreme power on his home ground, the 27-year-old produced a show of extreme power to blitz eleven fours and two sixes in his 66-ball knock of 84, putting on 126 in 17.4 overs with opening partner Jonny Bairstow to set a flawless platform for the chase.
"We are caught between Test cricket and T20 cricket - of course we're very good at T20 cricket and we're ever-improving in the Test match arena", added Law, whose side recorded a shock win over England in the second Test at Headingley last month before losing a three-match series 2-1.