The English bowlers restricted the West Indies to 180-4 on the same pitch on which the co-hosts had scored 218 against Afghanistan on Monday.
Opener Phil Salt He then scored 87 runs in 47 balls to give the team the lead and the batsmen completed the task within 18 overs.
Having progressed to the second stage by the slenderest margin on net run rate, beating one of the best-form teams in the tournament will be a huge confidence booster for England.
They now top Group 2 along with South Africa, who they will face at the same venue on Friday.
The credit for this victory largely goes to the England bowlers, who prevented the local batsmen from demonstrating their full potential.
He bowled 51 dot balls and took regular wickets in the second half of the innings, ensuring that no West Indies batsman reached half-century.
Despite the loss of opener Brandon King for 23 with a groin injury, West Indies were confident of posting a big score and had reached 82 for no loss by the middle of their innings.
However, just as they were trying to score quickly, the other opener, johnson charlesGot caught in the trap and was caught in the deep off Moeen Ali for 38.
key players Nicholas Pooran and captain Rovman Powell both scored 36 runs before being dismissed in successive overs, followed by Andre Russell also dismissed for a single in the next over, leaving West Indies at 143–4 in the 17th over.
Sherfane Rutherford (28 not out) and Romario Shepherd added a further 37 runs but England believed the target was reachable, especially after Salt and Jos Buttler added 67 for the first wicket.
Buttler fell to the off-spin of Roston Chase for 25, but Salt kept up the run-scoring pace before he was dismissed for 25. Jonny Bairstow,
Initially, Salt allowed Bairstow (48 not out) to take the strike but then he smashed 30 off Shepherd in the 16th over with the help of three sixes and three fours to effectively ensure the chase.