Johnson Charles went after the Lankan bowlers and scored a half-century
Charles and Darren Bravo added 70-run stand before the latter was dismissed.
West Indies had a stuttered start after winning the toss and opting to bat in overcast conditions as Sri Lankan bowlers reduced them to 29 for 2.
Charles's good innings was brought to an end on 83 (70) before rain halted play for a long period.
With the match shortened to 38 overs-a-side, Marlon Samuels's 63 (61) helped West Indies post 214. As per D/L method, Lanka needed 225 to seal the series.
Lahiru Thirimanne joined forces with Perera to power Lanka in their chase
Perera soon reached his fifty and was on course for a well-paced century but fell run short of it.
Despite Perera's departure, Thirimanne continued to score his runs and finished unbeaten on 81 as Sri Lanka won by eight wickets.
Kusal Perera led Sri Lanka's rebuilding charge
West Indies put early pressure on the Lankans with the wicket of Dilshan