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, who scored a century in the rain-hit opening match, was trapped leg-before for 12 by Nuwan Kulasekara, while Muralitharan removed Gayle (28) with his first delivery.
Gayle played some aggressive shots in his 30-ball cameo, smashing seamer Angelo Mathews for three fours in an over and then hitting Kulasekara for a four and a six off successive balls in the next over.
Darren Bravo put on 49 for the third wicket with Ramnaresh Sarwan (21) and 38 with Dwayne, but fell when looking well-set. He hit two sixes off Muralitharan and one off left-arm spinner Rangana Herath before being trapped leg-before by Malinga, who struck again when he bowled Kieron Pollard for four in his next over.
The series precedes the World Cup, which opens in India, Sri Lanka and Bangladesh on February 19.
Scoreboard in the second one-day international between West Indies and Sri Lanka at Sinhalese Sports Club in Colombo today.
West Indies:
C Gayle c Samaraweera b Muralitharan 28
A Barath lbw b Kulasekara 12
Darren Bravo lbw b Malinga 39
R Sarwan run out 21
Dwayne Bravo b Herath 39
K Pollard b Malinga 4
C Baugh not out 28
D Sammy run out 4
N Miller c Jayawardene b Muralitharan 0
R Rampaul b Malinga 1
K Roach b Kulasekara 9
Extras: (B-1, LB-8, W-9) 18
Total: (all out; 50 overs) 203
Fall of wickets: 1-45, 2-45, 3-94, 4-132, 5-138, 6-175, 7-187, 8-187, 9-192, 10-203
Bowling: Malinga 10-0-30-3, Kulasekara 10-1-42-2, Mathews 4-0-20-0, Muralitharan 10-2-42-2, Dilshan 7-0-27-0, Herath 9-1-33-1.
Sri Lanka (Revised target 197 off 47 overs):
U. Tharanga not out 101
T. Dilshan c Baugh b Rampaul 11
K. Sangakkara c Gayle b Dwayne Bravo 20
M. Jayawardene not out 48
Extras (lb-3, w-16) 19
Total (for two wickets in 42.3 overs) 199
Fall of wickets: 1-32, 2-102.
Bowling: Rampaul 7-0-27-1, Roach 8-0-29-0, Sammy 9-0-42-0, Gayle 4-0-18-0, Dwayne Bravo 5-0-29-1, Miller 6.3-0-33-0, Pollard 3-0-18-0.