The hosts are still trailing by 245 runs in the match at Zahur Ahmed Chowdhury Stadium.
Bangladesh lost their first wicket without posting anything on the board when Shadman Islam was caught behind the wicket off Yamin Ahmadzai. Soumya Sarkar and Liton Das tried to repair the initial blow adding 38 in 19 overs.
But they failed to bring the team to a safe zone. Soumya missed the line while playing Mohammad Nabi and dismissed for 17 off 66.
Liton and Mominul Haque added 16 runs in the third wicket stand, but it was Liton who fell as the third wicket for 33. He missed the length of that delivery of Rashid Khan and saw his stumps shattered.
After Liton, Rashid removed Shakib Al Hasan (11) and Mushfiuqr Rahim (0) as well. Shakib was pinned on his pad while Mushfiqur was caught close to the wicket, and eventually, Bangladesh lost five wickets at Tea of day two.
Rashid bagged three wickets just in five overs conceding 16 runs while Yamin and Nabi took one wicket each so far.
Earlier, riding on the maiden Test ton of Rahmat Shah (102) and a superb 92 of Asghar Afghan, Afghanistan posted 342 - their highest total in Tests.
For Bangladesh, Taijul Islam bagged four wickets while Shakib and Nayeem Hasan took two wickets each.