The hosts, who had already won the five-match series, went 4-0 in front thanks to a 134 fifth-wicket stand between Mahmudullah and Mushfiqur Rahim (77).
The Tigers were struggling on 32 for four when the pair came together and moved??on to 166 by the time Rahim fell. They reached 256 for eight from their 50 overs and it proved enough as they restricted Zimbabwe to 235 for eight.
Neville Madziva and Solomon Mire, who both finished with three wickets apiece,??rattled through the Bangladesh openers, reducing the hosts from 31 for one to 32??for four. But Mahmudullah and Rahim turned the match firmly back in the favour of their??side, though.
The latter hit seven fours in his 78-ball knock before he was caught at cover??by Elton Chigumbura off Tafadzwa Kamungozi.
Mahmudullah, whose innings featured six fours and lasted 112 balls, then saw??partners come and go, but Mashrafe Mortaza bashed 39 off 25 to boost the total.
A century partnership between Brendan Taylor and Mire for the fourth wicket??gave the tourists hope, Taylor making 63 and Mire 52.
Mire was dismissed with Zimbabwe 90 runs adrift of their opponents’ total, with??Taylor following the next over, just six runs later.
And no one was able to provide a late flourish in the manner of Mortaza as??Bangladesh closed out another win.
The fifth ODI will be held at the same venue on December 1.