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 wait on World Cup progress after draw with Egypt
Iran face an anxious wait to see if they will progress to the World Cup knockout stages after they held Egypt to a 1-1 draw and finished third in Group G on Friday.
Belgium beat New Zealand 5-1 to advance to World Cup knockout stage
Leandro Trossard scored twice as Belgium beat New Zealand 5-1 to breeze into the knockout stage of the World Cup, winning Group G to set up a last-32 clash with one of the eight best third-placed teams.
Baena strike sends Spain past Uruguay into World Cup knockouts
Spain edged Uruguay 1-0 on Friday to top Group H and reach the knockout stage of the World Cup, with Alex Baena's first-half strike enough to settle a tense, physical contest and leave Marcelo Bielsa's side out of the tournament.
Jubilant Cape Verde set date with Argentina in World Cup round of 32
Debutants Cape Verde prolonged their World Cup fairytale on Friday as they secured a place in the World Cup round of 32 following a 0-0 draw with Saudi Arabia to set up an unexpected clash with defending champions Argentina in Miami.
Senegal ring up 5-0 win over 10-man Iraq, keep knockout hopes alive
Substitute Pape Gueye scored a pair of sensational second-half goals from long range, and Senegal got a much-needed boost for their goal differential with a 5-0 victory over 10-man Iraq in their Group I finale on Friday in Toronto.
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