Ishant Sharma made an electrifying start to the innings, claiming two early wickets of opener Jeremy Solozano (9) and first-down Brandon King (4) in his first spell of five overs, while Umesh Yadav too found his rhythm early, dismissing Darren Bravo during his five overs giving away just seven runs.
Opener Kavem Hodge (51), who was dropped at slips in the third over, held on to one end but regular loss of wickets at the other end affected the hosts' innings.
Hodge was also removed by Ishant Sharma, before Kuldeep Yadav and Umesh Yadav swept the lower-middle order. Kuldeep dismissed Jonathan Carter on 26, while Umesh rattled the Windies tail, taking off Rovman Powell, Romario Shepherd and Khary Pierre.
Earlier after a delayed start due to rain, India declared their first innings at the overnight score of 297 for five.
In reply, opener Solozano was the first to leave after his flat-footed drive found an edge and landed in the safe hands of KL Rahul as West Indies slipped to 16 for one in 4.2 overs.
King (4) was then dismissed in the ninth over when he played a loose drive only to be caught behind by Rishabh Pant as West Indies slipped to 30 for 2.
Bravo (11) then tried to stitch a partnership with Hodge but after adding 21 runs he edged an Umesh Yadav delivery to second slip with Rahul completing the formality.
In the 27th over, a direct throw from mid-on by Ravindra Jadeja ended the brief stint of Jason Mohammed (6) as West Indies A were reduced to 77 for four in 26.1 overs.
Ajinkya Rahane, who failed in the first innings, promoted himself up the order in the second, as he opened the innings alongside Mayank Agarwal. While Agarwal failed to make a mark, caught-behind on 13, Rahane (20*) and Hanuma Vihari (48*) remained unbeaten as India finished the day on 84/1 in 35 overs.
Pujara and Rohit stitched 132 runs together for the fourth wicket to take India to a strong position after being reduced to 89 for 3 at lunch on Saturday.
Test specialist Pujara got going in his first competitive match of the West Indies tour as he retired after making 100 off 187 balls during which he struck eight fours and one six.
Rohit fell after making 68 off 115 balls. He hit eight fours and one six.
After Pujara retired in the final session, Pant and Hanuma Vihari pushed the Indian total further to reach near the 300-run mark.
Stumps were drawn just after Pant was out for a 53-ball 33 which he made with the help of four boundaries and one six.
Vihari was batting on 37 from 101 deliveries while Jadeja was on 1 when the stumps were drawn after playing 88.5 overs.
For West Indies A, pacer Jonathan Carter took 3 wickets for 39 runs from his 13.5 overs, while Keon Harding and Akim Frazer got one wicket apiece.
India 1st Innings: 297/5 from 88.5 overs declared (Pujara 100 retired, Rohit Sharma 68, Rishabh Pant 33, Hanuma Vihari 37 not out; Jonathan Carter 3/39)
West Indies 1st innings: 181 in 56.1 overs (Kavem Hodge 51; Umesh 3/19, Ishant 3/21, Kuldeep 3/35).
India 2nd Innings at the end of the day: 85/1 in 34 overs (Vihari 48*, Rahane 20*; Shepherd 1/3)
(With inputs from PTI)