Ramesh Mendis spearheaded the Sri Lankan attack to restrict West Indies to 253 in the first innings of the second Test match at the Galle International Cricket Stadium.
Mendis finished with impressive figures of 6/70 to go with his seven-wicket haul in the first game of the series.
Spinners Lasith Embuldeniya and Praveen Jayawickrama picked up two wickets apiece. For the visitors, skipper Kraigg Brathwaite top scored with 72.
Jermaine Blackwood hit 44 while Kyle Mayers remained unbeaten on 36.
West Indies now has a substantial 49-run lead after dismissing Sri Lanka for 204 in the first innings.
The Lankans lead the two-match series 1-0 after winning the opening game at the same venue.