Bangladesh won the second game in the five-match series by 63 runs after Zimbabwe beat the visitors by two wickets at the same venue on Saturday.
Farhad Reza's 50, which he scored off 57 balls with four fours and a six, was Bangladesh's top score in their total of 238 for seven.
In reply, Zimbabwe were bundled out for 175 in 44.4 overs.
Fast bowler Shahadat Hossain struck up and down the order and took three for 41 from 7.4 overs.
Shahadat was well supported by medium pacer Abdur Razzak, who took two for 28, and left-arm spinner Mohammad Raique, who claimed two for 24 from 10 overs.
The visitors lost wickets steadily after being put in to bat, although a smashed 40 off 25 balls by number three Aftab Ahmed kept the runs flowing.
Bangladesh were reduced to 76 for five in the 20th over before Khaled Mashud joined Reza to add 71 runs for the sixth wicket.
Mohammad Rafique, who scored 32, helped Mashud to add 48 for the seventh wicket.
The experienced Mashud marshalled the Bangladesh tail well to finished with an unbeaten 48.
Medium pacer Blessing Mahwire took three for 29, equalling the career-best figures he took against Bermuda in Trinidad in May.
Zimbabwe also sacrificed wickets too readily, and it was left to opener Vusi Sibanda to hold the innings together with his 33 off 61 balls.
Sibanda's dismissal in the 18th over saw Zimbabwe slump to four for 71, and Stuart Matsikenyeri's 46 was the home side's only other noteworthy innings.
Zimbabwe's serious hopes of winning were dashed when Matsikenyeri's dismissal reduced them to 146 for seven in the 40th over.