The hosts, who started their innings with a lead of 299, lost two early wickets but Pujara and skipper Virat Kohli (38) put on 67 runs.
Left-arm spinner Shakib Al Hasan checked India's surge with two wickets including that of Kohli, who doled out a catch to mid-wicket in his search for boundaries.
Pujara hit six fours and a six during his 58-ball stay.
Earlier Sunday India's off-spinner Ravichandran Ashwin became the fastest bowler to claim 250 Test wickets as Bangladesh were bowled out for 388. The hosts did not enforce the follow on.
Ashwin achieved the milestone in his 45th match by taking the final wicket of the innings -- Bangladesh skipper Mushfiqur Rahim.
Rahim had led Bangladesh's resistance for nearly three sessions with his patient 127 before falling foul of 30-year-old Ashwin, who surpassed Australia paceman Dennis Lillee's record. Lillee took 48 matches to reach the same mark.
Ninth-ranked Bangladesh are playing their first Test on Indian soil.