Kulasekara recorded figures of 2 for 37 in his 10 overs but also effected two run-outs, ensuring that the West Indies were unable to gather any serious momentum in their innings and were bowled out in 49.2 overs.
Returning to the Sri Lankan side for the first time in 10 months, Kulasekara had taken two key wickets as the tourists beat hosts Zimbabwe by eight wickets in Monday's series opener, and on Wednesday he played another key role.
Kulasekara went on to run out West India captain Jason Holder with another direct hit towards the end of the innings, before trapping Sulieman Benn lbw.
Shorn of their biggest stars, including batsman Darren Bravo after he was sent home for comments made on twitter about West Indies Cricket Board president Dave Cameron, the West Indians lacked impetus in their innings after they lost the toss and were asked to bat.
Although conditions were challenging early on, with Sri Lanka's seamers exploiting lateral movement to good effect, the West Indies failed to show the required urgency during the middle overs.
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