Jason Roy and captain Joe Root both smashed centuries as the tourists easily reached their target of 361 with eight balls to spare in Barbados.
It was their highest ever run-chase in the format.
Chris Gayle's innings of 139 off 129 balls went in vain as the Windies' poor form in ODI cricket continued.
The second encounter of the five-match series will be played on Friday.
Brook's defiant ton in vain as New Zealand beat England
New Zealand overcame a blitz from centurion Harry Brook to beat England by four wickets on Sunday in the opening game of their three-match one-day international series, with Daryl Mitchell and Michael Bracewell scoring half-centuries.
Bencic tames Noskova to win Tokyo title
Belinda Bencic breezed past Czech sixth seed Linda Noskova 6-2 6-3 to win the Pan Pacific Open title on Sunday, erasing bitter memories of her straight-sets defeat by Agnieszka Radwanska in the title clash of the same tournament 10 years ago.
We need to find answers to stop Liverpool slide, says Slot
Liverpool manager Arne Slot said opponents have identified a winning strategy against his Premier League champions and he needs to find a solution fast after a 3-2 defeat at Brentford on Saturday made it four league losses in a row.
Rohit and Kohli bid likely farewell to Australia as winners
Rohit Sharma hit a century and Virat Kohli a bright 74 to drive India to a nine-wicket win in the third one-day international on Saturday, sending fans home happy after what are likely to be their final appearances in Australia in their country's colours.
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