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.

Mac Allister heads Liverpool to Champions League win over Real Madrid
Sabalenka overpowers Pegula, Gauff eliminates Paolini in WTA Finals
Pakistan win ODI against South Africa in last over as Salman shows the way
David Beckham knighted for services to sport and charity
Aryna Sabalenka challenges Nick Kyrgios in Dubai showdown
