The tourists lost Shivnarine Chanderpaul for 54 and Dwayne Bravo without scoring to reach 244-5 before play was halted prior to the scheduled tea interval with Brendan Nash unbeaten on 62 and Carlton Baugh on naught.
Sri Lanka made a vital breakthrough soon after lunch by ending a 99-run fourth wicket stand between Chanderpaul and Nash.
Ajantha Mendis removed the defiant Chanderpaul when Mahela Jayawardene pulled off a brilliant diving catch at slip, inches off the ground.
Seven balls later left-arm spinner Rangana Herath, who was brought into the attack rather late in the innings, made up for lost time by taking the wicket of Dwayne Bravo.
Wicketkeeper Prasanna Jayawardene brought off a smart stumping when Bravo charged forward but missed the sharp-turning ball.
The wicket of Darren Bravo was all hosts Sri Lanka had to show for their morning's work as West Indies reached 229-3 at lunch.
West Indies, resuming on 134-2, went into lunch with fourth-wicket pair Chanderpaul and Nash putting together an unbroken stand of 87 off 173 balls.
Nash reached his half-century before the break off 74 balls, with five fours helping him to 55. Left-hander Chanderpaul played the anchor role, batting throughout the session to 46.
Chanderpaul survived a suicidal reverse sweep shot off left-arm spinner Rangana Herath at 38.
The umpire ruled him out lbw but he successfully challenged the decision, the replay showing the ball clearly hit his gloves.
There was no such luck for Bravo, however, who added only five runs to his overnight score of 63 before Dilhara Fernando trapped him lbw in the fourth over of the day.
Bravo asked for a referral but the ball was shown to have thudded into his pads, hitting him between leg and middle.
The three-match series is tied at 0-0 after the first two Tests were drawn.
