Shafiul Islam, Rubel Hossain, Jubair Hossain and Shuvagata Hom claimed two wickets apiece as Zimbabwe, chasing 449, crumbled to 262 all out on day five.
Regis Chakabva offered the main resistance with 89 not out, although his effort proved in vain.
Zimbabwe, who began the day on 71-1, were undermined quickly as Hamilton Masakadza gloved a reverse-sweep from Shuvagata straight to the wicketkeeper and captain Mushfiqur Rahim.
Shuvagata did not have to wait too long for a second wicket, with Sikandar Raza clubbing a full-toss straight to deep midwicket.
Chakabva and Brendan Taylor rebuilt somewhat thereafter, putting on a 49-run stand.
However, the latter would eventually depart for 24, Jubair luring him into an ill-advised drive that flew straight to point.
Elton Chigumbura did not last too long, compiling 16 before edging Jubair to first slip - where Imrul Kayes took a superb low catch.
All the while, Chakabva was battling as he mixed a solid defence with the odd moment of intent.
But wickets continued to tumble at the other end, Craig Ervine, Richmond Mutumbami and Tinashe Panyangara falling lbw to Mahmudullah, Taijul Islam and Rubel respectively.
And Shafiul finished the job when trapping Natsai M'shangwe lbw after castling Shingi Masakadza earlier in the over, leaving Chakabva unbeaten at the other end.