West Indies trail the hosts by 180 runs with seven wickets remaining in their second innings.
Pujara notched up an unbeaten 306 in a masterly exhibition of batsmanship as India A declared their first innings at 564 for nine just at the stroke of tea in reply to West Indies A's 268 in their first essay, to take a substantial 296-run lead.
At stumps on day three, the Indians had reduced the visitors to 116 for three in their second innings at KSCA Stadium.
Right-arm medium fast Ishwar Pandey claimed the prized wicket of Kraigg Brathwaite leg before for 21. The right-hand batsman had been a thorn in the flesh for the hosts with two half centuries and a century in the series.
More From This Section
Narsingh Deonaraine and Assad Fudadin were batting on 44 and 36, respectively, when the stumps were drawn. The duo had put on an unbeaten 59 runs together for the fourth wicket.
Captain Pujara, who became only the second Indian after Ravindra Jadeja to score three triple hundreds, would be expecting Zaheer, Abhishek Nayar and Kulkarni to come good and help India A level the three-match series 1-1.
The day today belonged to the Saurashtrian run-machine Pujara, who displayed an innings of discipline and character to tilt the match in India A's favour.