Despite facing a moderate target, the tourists never recovered from the loss of skipper Chris Gayle and Marlon Samuels to successive deliveries from Lungley and threw away wickets with a series of loose strokes.
Opener Chris Gayle made 75 and Jamaican local Marlon Samuels hit nine fours and two sixes in a 91-ball century before retiring as the home side posted 268-4.
The pair rescued the West Indies, who had slipped to 91-3 in the 23rd over after losing Marlon Samuels for nine, Ramnaresh Sarwan for six and Chris Gayle for 46.