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.

Iran will be at World Cup and will play in the US, says FIFA boss
Abu Dhabi advises fans to arrive early for Al Ain, Al Wahda match
Sangakkara, Mahanama named in interim committee to run Sri Lanka Cricket
Focused Fils making a statement ahead of French Open
Atletico hit back to hold Arsenal in cagey Champions League semi-final first leg
