Set a target of 119 to win by the hosts at the Kensington Oval, England set about their task in brisk fashion and appeared on course to gain revenge for their defeat earlier in the tournament.
But it came down to the final over and needing four to win off the last ball, England could only manage three, sending the match to a decisive super over.
England scored six for the loss of one wicket in their over, but the West Indies knocked them off with ease, sealing victory with a boundary.
The two teams had already qualified for Saturday's final after finishing ahead of New Zealand in the table.
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