Fast bowler Nahid Rana took 4 for 26 as Bangladesh restricted Zimbabwe to 170 for 6 in the opening T20I at Queens Sports Club in Bulawayo on Wednesday.
After Bangladesh captain Towhid Hridoy won the toss and chose to field, Zimbabwe reached 54 for 1 in the powerplay.
Brian Bennett led the scoring with 44 from 30 balls, while Tadiwanashe Marumani made 14 from 9 deliveries.
Nahid struck in the fourth over when Marumani was caught at deep square leg attempting a flick. Zimbabwe were 87 for 2 at the halfway stage with Bennett and Sikandar Raza at the crease.
Bennett fell for 44 when he slashed a short, wide delivery from Nahid to deep backward point in the 11th over.