Zimbabwe started out slowly as opener Brendan Taylor was run out by Shohrawardi Shuvo for no runs in the first over of the day. Mortaza (2-25) then trapped Hamilton Masakadza lbw for 6 runs and dismissed Keith Dabengwa lbw for 9.
After losing the three early wickets, Craig Ervine (46) and Tatenda Taibu (64) tried to rally Zimbabwe in their partnership before Ervine was caught by Mushfiqur Rahim off an Al Hasan delivery.
The visitors lost their momentum when Taibu was dismissed, caught by Mortaza off Al Hasan, and Elton Chigumbura (23) was caught by Raqibul Hassan.
Zimbabwe won the first match and Bangladesh took the second and third. The fourth match was abandoned due to a wet outfield.