England resumed in Barbados 107 ahead at 39-5 but, despite an unbeaten 35 from Jos Buttler, were all out for 123.
It left the hosts with a target of 192 and they were 80-4 before Darren Bravo and Jermaine Blackwood shared 108.
Left-hander Bravo struck three sixes in a magnificent 82 and Blackwood was 47 not out as the hosts beat England for only the second time in 29 Tests.
