Chasing a target of just 200, Bangladesh made light work of the run-chase with Tanzid Hasan hitting 94 while Soumya Sarkar scored 69 as the pair shared in an opening partnership of 151.
While both players lost their wickets towards the end it mattered little the Tigers knocked off the target with 14 overs to spare.
Zimbabwe were earlier bowled out for just 199 with Wessly Madhevere top-scoring with 75 while Brad Evans (50), batting at number 8, scored his second consecutive half-century.
The hosts, who were inserted to bat at the toss, were in trouble at 108-6 in the 34th over but Madhevere and Evans made an effort for a rescue act but ultimately was not enough.
Bangladesh's seamers came to the fore with Shoriful Islam taking 4-44 while Taskin Ahmed and Tanvir Islam took two wickets apiece.
Zimbabwe won the three-match series 2-1 with the first of three T20Is set take place in Bulawayo on Wednesday.
Bangladesh paceman Mustafizur Rahman has been ruled out for the remainder of the tour to Zimbabwe due to a grade 1 muscle tear in his right hamstring and a meniscal degeneration in his right knee.
Zimbabwe have largely stuck with the squad that reached the Super 8 stage of the T20 World Cup earlier this year for the upcoming three-match home series against Bangladesh.
Zimbabwe fast bowlers Richard Ngarava and Newman Nyamhuri scored vital lower-order runs and then shared five wickets as the home side edged Bangladesh by 25 runs in the first of three ODIs in Harare.
Sikandar Raza has returned to Zimbabwe's squad for the three-match ODI series at home against Bangladesh after missing the one-off Test match due to T20 commitments in England.
