Brian Lara was not out 93 when play was stopped eight overs after the lunch break, with Marlon Samuels on five.
Off spinner Muttiah Muralitharan claimed a single wicket for Sri Lanka early in the afternoon session before the rain intervened.
Ramnaresh Sarwan (7) tried a pull shot, but the ball ballooned off the boot of short fine leg Kumar Sangakkara and Marvan Atapattu took the catch.
However video replays suggested the ball had hit the ground before making contact with Sangakkara's foot.
Wavell Hinds struck a solid 113 in the morning session before being the victim of a mix-up with Lara that gave Atapattu an easy runout opportunity for Sri Lanka.
The third-wicket stand of 174 between Hinds and Lara had put West Indies on top after the home side began the day on 161 for two.
"It was a nice feeling to score a century again for the West Indies," said Hinds, who had been out of favour with the West Indies selectors but was recalled for the Sri Lanka series when Shivnarine Chanderpaul was ruled out with a broken finger.
"Obviously it's all in the cause of helping the team get into a winning position, given the nature of the wicket and the state of the game right now," the left-handed batsman added.
West Indies have so far batted for 74.2 overs in their innings and play is scheduled to start 30 minutes earlier on Monday to compensate for lost time.
