West Indies was bowled out for 203 in 50 overs after being asked to bat first by Sri Lanka captain Kumar Sangakkara at the Sinhalese Sports Club.
After a brief rain interruption, Sri Lanka was given a revised target of 197 in 47 overs under the Duckworth/Lewis method and reached it with 27 balls to spare.
Sri Lanka leads the three-match series 1-0 after the first match was abandoned due to bad weather.
Tharanga, who was named man of the match, said his innings had served as a good warm-up for the World Cup.
“I am pretty pleased to score some runs. There were some issues about the opening slots,” said left-handed Tharanga, who was picked ahead of veteran Sanath Jayasuriya for the World Cup.
Sri Lanka lost opener Tillakaratne Dilshan with the total on 32, caught behind by Carlton Baugh off seamer Ravi Rampaul for 11 runs.
Sangakkara joined Tharanga for a useful 70-run partnership to seize the initiative before Sangakkara was caught by Chris Gayle off seamer Dwayne Bravo for 20.
The best partnership of the day, an unbeaten 97 runs, came between Tharanga and Mahela Jayawardene to seal victory.
Tharanga said his role in the World Cup would be to bat through the innings.
“The team management and the captain had a chat with me and said that what they expect from me is to bat until 40 or 45 overs,” he said. “They said they would be happy if I get 80 or 90 runs by that stage and that's what I am trying to do.” Tharanga executed this role perfectly Thursday as he laid anchor and batted through the innings to finish with 101 not out off 143 balls including seven boundaries.
Jayawardene made a brisk 48 not out in 46 balls with five boundaries.
West Indies' innings started with promise but Sri Lanka's bowlers, led by Lasith Malinga, deprived them of a big score.
After the visitors lost both in-form opener Adrian Barath and Gayle with the score on 45, the bowlers took crucial wickets to end several promising partnerships, and put the home side in a winning position.
Barath, who scored 113 for a maiden ODI century in the previous match, was trapped lbw by seamer Nuwan Kulasekara and off spinner Muttiah Muralitharan snared Gayle with his first ball, caught at slip by Thilan Samaraweera. Gayle made 28 in 30 balls including four boundaries and a six.
Darren Bravo and Ramnaresh Sarwan shared a valuable 49-run stand for the third wicket before Sarwan was run out to a straight drive by Bravo which hit the stumps after touching the bowler's fingers.
Bravo hit three sixes in his 39 runs while his half-brother Dwayne Bravo also made 39 to become top scorers for the West Indies.
Malinga who took the wickets of Darren Bravo, Kieron Pollard and Ravi Rampaul, finished with 3-30 while Muralitharan and Kulasekara also picked up two wickets each.
