Shubman Gill struck a maiden century as India declared their second innings at 258-2 to set Bangladesh a daunting 513-run target to win the first Test in Chittagong on Friday.
Skipper KL Rahul called back his batsmen after Cheteshwar Pujara also brought up his 19th Test hundred with a four off Taijul Islam in the third session of the third day.
Pujara, who scored 90 in India's first-innings 404, was unbeaten on 102 having smashed 13 fours when the declaration came, with former skipper Virat Kohli 19 not out at the other end.
The 23-year-old Gill, playing in his 12th Test match, earlier completed his maiden century before he was dismissed by Mehidy Hasan for 110.
Gill, who hit 10 fours and three sixes, shared 113 runs for the second wicket with Pujara after Rahul holed out to Taijul Islam at fine leg off Khaled Ahmed.
Rahul had decided not to enforce the follow-on after India bowled out Bangladesh for 150.
Left-arm spinner Kuldeep Yadav led India's bowling attack with career-best figures of 5-40, his third five-wicket haul in Tests.
India needed barely an hour of the third day to mop up the Bangladesh tail after the hosts resumed on 133-8.
Axar Patel took the last Bangladesh wicket of Mehidy Hasan, who offered some late resistance before being dismissed for 25 in the 12th over of the morning.
Fast bowler Mohammed Siraj took 3-20 as India dominated.
Mushfiqur Rahim top-scored for the deflated hosts with 28 before he became one of Kuldeep's victims, out lbw.
In India's first innings Shreyas Iyer and Ravichandran Ashwin also scored 86 and 58 runs respectively.
Off-spinner Mehidy claimed 4-112 for Bangladesh while left-arm spinner Taijul took 4-133.