The South Asians hit back from a seemingly poor 238-8 to bowl out their African hosts for a meagre 175 here on Sunday.
Shahadat Hossain took three for 43 while Abdur Razzak claimed two for 28 and Mohammad Rafique weighed in with two for 24 as Zimbabwe's batsmen failed to deal with a fiery Bangladeshi attack.
Vusi Sibanda (33) and Stuart Matsikenyeri (46) were the only two batsmen to put up any form of resistance as Hossain and Razzak ripped through the Zimbabwe top order.
Hossain took two early wickets and when Razzak took the wicket of Sibanda, the writing was on the wall for the Africans.
The middle order countered but once Matsikenyeri, who along with was caught by Khaled Mashud off Razzak, the end came quickly.
A debut 50 from Farhad Reza and an undefeated 48 from veteran Mashud were the foundations for Bangladesh.
They endured a sluggish start with opener Javed Omar dimissed for just 10 and fellow opener Shahriar Nafees, who had top-scored with 78 in the first match, out for only seven.
Aftab Ahmed made a quickfire 40 which included two sixes and five fours.
Farhad and Mashud put on 71 for the sixth wicket after their side had been reduced to 76 for 5 at one stage.
Rafique hit 33 off 44 deliveries in the closing stages.
Best Zimbabwe bowler was seamer Blessing Mahwire who took 3-29 off eight overs.