Mehidy Hasan struck thrice while Shakib Al Hasan claimed two wickets after Bangladesh posted a mammoth score of 508 runs in their first innings.
Mahmudullah Riyad was the top contributor for the hosts with the bat scoring a career best 136. Useful contributions from Shakib (80), Shadman Islam (76) and Liton Das (54) helped Bangladesh go beyond the 500 runs mark.
The West Indies innings tottered right from the start as Shakib claimed a wicket in the very first over, bowling Kraigg Brathwaite for zero.
Kieran Powell (four), Sunil Ambris (seven), Roston Chase (zero) and Shai Hope (10) followed in quick session that saw the visitors precariously placed at 29 for five.
However, Shimron Hetmyer (32 not out) and Shane Dowrich (17 not out), stemmed the slide by putting up an unbeaten partnership of 46 runs for the sixth wicket.
All five West Indies batsmen were clean bowled – only the third time in cricket history and the first time by spinners.
Bangladesh lead the two-Test series 1-0 following their 64-run win in the first Test in Chittagong.