The West Indies bowlers pegged Sri Lanka to 250-8 on Wednesday as rain interrupted play throughout the third day’s play in Antigua.
The hosts resumed their first-innings score on 136-3 but lost the early wickets of overnight batsmen Dinesh Chandimal (44) and Dhananjaya de Silva (39).
Pathum Nissanka and Niroshan Dickwella looked solid with the bat but the latter fell for 20 when he was dismissed by Jason Holder.
Alzarri Joseph then sent Suranga Lakmal packing for only six before Holder got rid of Dushmantha Chameera for two.
With rain interfering throughout the afternoon, the Sri Lanka batsmen struggled for worthy partnerships. Nissanka, though, will start Thursday’s action unbeaten on 49.