Bangladesh were all out for 233 in their first innings against India in the second Test in Kanpur on Monday.
Mominul Haque made 107 not out, his 13th Test hundred, but did not get much support from his teammates.
Jasprit Bumrah (3/50) was the pick of the Indian bowlers. India are 1-0 ahead in the two-Test series.
Bangladesh's top order collapsed as they resumed day four on 107/3, after rain and a wet outfield did not allow play in the prior two days of the contest, which appears to be heading for a draw.
Mushfiqur Rahim (11) shoulder-armed to an incoming ball from Bumrah only to hear the sound of the ball crashing onto his stumps.
India's superb catching led to the next two dismissals.
Litton Das (13) hit Bumrah for three fours in an over but Rohit Sharma leapt at mid-off and grabbed a stunning one-handed catch to remove the batter, who had charged at Mohammed Siraj.
Siraj showed similar athleticism to remove Shakib Al Hasan for nine, running backwards from mid-off and taking a tumbling single-handed catch after the batter had charged down the track against Ravichandran Ashwin.
Mominul survived some torrid moments too before bringing up his hundred with a swept four against Ashwin.
He was adjudged caught at square leg but the decision was overturned after he challenged it and replays confirmed the ball had bounced off his thigh guard.