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The left-handed opener hit seven fours in his ninth one-day century as Sri Lanka achieved a rain-revised target of 197 with more than four overs to spare for a 1-0 lead in the three-match series.
The opening game of the series was abandoned due to rain on Monday.
The final match will be played on Sunday.
Tharanga added 70 for the second wicket with skipper Kumar Sangakkara (20) and 97 for the next with Mahela Jayawardene (48 not out) to ensure his team's comfortable victory.
Former captain Jayawardene finished the match when he cut spinner Nikita Miller for his fifth boundary.
Sri Lanka were earlier indebted to paceman Lasith Malinga (3-30) and off-spinner Muttiah Muralitharan (2-42), who bowled the tourists out for a modest 203 at the Sinhalese Sports Club in Colombo.
Half-brothers Darren and Dwayne Bravo scored 39 each.
The West Indies, put in to bat, put on 45 for the first wicket before losing openers Chris Gayle and Adrian Barath in the space of three balls. Barath, wh