At the interval, Mominul Haque was on 59 — becoming the fourth batsmen to score a half-century in 11 consecutive tests — and Soumya Sarkar was on 1.
Fast bowler Imran Khan (2-37) and leg-spinner Yasir Shah (2-42) ran through the top order after the hosts resumed the day on 63-1.
Most of the Bangladesh batsmen threw way their wickets with impatient strokes.
Opener Tamim Iqbal scored 42 and was the first man out in the morning session when he nicked an Imran delivery to Sarfraz Ahmed. Shakib Al Hasan made 13.
Bangladesh secures 1st win vs England with 108-run victory