Having lost the toss, the West Indies posted a score of 172-5 before Sri Lanka were bowled out for 139 with four balls remaining.
Chris Gayle made just 12 at the crease, but it was Dwayne Smith (60) and Dwayne Bravo (43) who did most of the damage with the bat for the Windies. Darren Sammy also made a significant contribution with an unbeaten knock of 30.
Sri Lanka struggled out in the middle with the early dismissals of Kusal Perera (4) and Mahela Jayawardene (0), though Tillakaratne Dilshan (43) and Kumar Sangakkara (24) managed to boost their team's score.
However, the Sri Lankan bottom order made just 48 runs between them as the West Indies cleared up to claim the win.