Mahela Jayawardene scored a half-century to help Sri Lanka get to a respectable total.
But his stay at the crease came to an end when he edged Sunil Narine to wicketkeeper Denesh Ramdin. He was out after scoring 52.
Sunil Narine finished with four wickets from his 10 over.
Sri Lanka skipper Angelo Mathews remained not out on 55 to ensure the visitors finish on 208 all out.
Ravi Rampaul backed up Sunil Narine's effort with three wickets.
Chris Gayle notched his first ODI hundred against Sri Lanka as he led West Indies to a crushing six-wicket victory with more than 12 overs to spare. This was his 21st century.
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