Set 202 runs to win in 22 overs under fading light, the West Indies ended the final day Saturday at 12 for two wickets from 11 overs.
Opener Adrian Barath (8) was trapped lbw by spinner Ajantha Mendis and Chris Gayle (3) edged Tillakaratne Dilshan to Mahela Jayawardene at slip.
Sri Lanka earlier declared its second innings at 57-1 after dismissing the West Indies' first innings for 243 - 144 behind Sri Lanka's 387-9.
West Indies had resumed the final day on 165-5 after rain prevented any play on day four. But soon spinner Rangana Herath ran through their lower-middle order and the tail.
Overnight batsman Carlton Baugh recorded his second Test half-century, including six boundaries, and shared a promising 44-run partnership with Dwayne Bravo (20) who became Herath's first victim, stumped by Prasanna Jayawardene.
The visitors lost their last five wickets for 35 runs.
Left-handed Herath bowled Baugh for 50 with a variation that darted in to the right hander and had tailender Sulieman Benn caught at forward short-leg to finish with 3-76.
Mendis and seamer Suranga Lakmal picked up two wickets each.
Sri Lanka's brief second innings lasted just 15 overs before captain Kumar Sangakkara declared the innings closed.
The first Test was also drawn. The last match of the three-Test series will played at Pallekelle - a new venue constructed for next year's World Cup in central Sri Lanka.
