Bangladesh set a target of 176 runs before Zimbawbe, in the fourth T20 of the tri-nation series in Chattogram on Wednesday.
A dashing half century from Mahmudullah propelled Bangladesh to score 175 for 7. He scored 62 off just 41 balls hitting a boundary and five over boundaries.
Lito Das scored the second highest run, 38 while Najmul Hossain Shanto, Mushfiqur Rahim and Shakib Al Hasan collected 11, 32 and 10.
Earlier, Zimbabwe skipper Hamitlon Masakadza won the toss and opted to field first. The match started at 6:30pm.
Bangladesh: Najmul Hossain Shanto, Liton Das, Shakib Al Hasan (c), Mushfiqur Rahim, Mahmudullah, Aminul Islam, Afif Hossain, Mosaddek Hossain, Mohammad Saifuddin, Mustafizur Rahman, Shafiul Islam.
Zimbabwe: Brendan Taylor, Hamilton Masakadza (c), Richmond Mutumbami, Sean Williams, Ryan Burl, Tinotenda Mutombodzi, Regis Chakabva, Neville Madziva, Kyle Jarvis, Ainsley Ndlovu, Chris Mpofu.