Opener Liton Das starred with an unbeaten half-century as the Tigers reached the target of 120 for victory with 25 balls in hand at the Mirpur Sher-e-Bangla National Cricket Stadium in Dhaka on Wednesday.
Everything went according to plans for the hosts from the toss after they had won the one-off Test and three One-Day Internationals against the African side earlier during the visit.
Captain Mahmudullah opted to field first and the bowlers were able to restrict Zimbabwe to a meagre total of 119 for 7 in 20 overs despite an unbeaten innings of 59 runs off 45 balls by opener Brendon Taylor as they never allowed the other batsmen to gather momentum.
Al-Amin Hossain drew the first blood as Zimbabwe lost the other opener Tinashe Kamunhukamwe in the third over.
Zimbabwe could manage only 25 runs in the first five overs of power-play but Taylor and Craig Ervine (29 off 33) pushed up the soring rate with a 57-run stand.
Afif Hossain proved to be on the right track to fulfil his all-round ambitions with the wicket of Ervine in the 12th over.
Sikandar Raza was the only other Zimbabwean batsman to reach a double figure with 12.
Al-Amin and Mustafizur Rahman took two wickets each.
Mohammad Naim Sheikh (33 off 34) assisted Liton to get Bangladesh off to a terrific start.
After Chris Mpofu dismissed Naim to save his team from the embarrassment of a 10-wicket defeat, Soumya Sarkar (20 off 16) completed the task with the winning single.
