After the hosts' first innings ended at 336 all out, Delorn Johnson and Kevin McClean struck with new ball to leave the visitors reeling at 30 for three in their second essay, still 76 runs behind when lunch was called.
Rohit Sharma was batting on 2 while Manoj Tiwary was yet to open his account.
West Indies, in reply to India's first-innings total of 230, added 16 runs to their overnight score of 320 for eight.
With a healthy lead on their side, Johnson and McClean bowled aggressively to put the hosts on top.
Johnson, who has dismissed Abhinav Mukund four times on the tour so far, had his man again when he got the out-of-form batsman to edge one to keeper Devon Thomas. Mukund's sequence of scores on the tour read a poor 0, 0, 8, 8, 10 and 20.
The Chennai batsman's dismissal brought the rain, forcing the players to walk off the field at the Beausejour Stadium.
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On resumption, India were dealt a blow again as Ajinkya Rahane had no answer to a perfect outswinger by Johnson.
India were 23 for two when Rahane gave Thomas his second catch of the day.
There was another setback in store for the visitors as in-form skipper Cheteshwar Pujara too failed to make a substantial contribution, thanks to a brilliant catch by Kieran Powell at gully off McClean's bowling.
Johnson had taken two for 13 while McClean had one for 16 in the first session.
Earlier, Parvinder Awana and Shami Ahmed took a wicket apiece to dismiss West Indies 'A' quickly on the third morning.
Awana and Jalaj Saxena finished with three wickets each while Ahmed struck twice. There was also a wicket for Akshay Darekar.