Ryan Burl slammed 57 in 32 balls, including 30 off a Shakib Al Hasan over, to help Zimbabwe make 144 for 5 in the first game of the tri-nation series in Dhaka on Friday.
The match has been curtailed to an 18-over affiar as continuous rain delayed the start of the game.
Burl hit three fours and three sixes in the 16th over bowled by the Bangladesh captain. He and Tinotenda Mutombodzi added 81 in the six-wicket, with the latter contributing 27 in 26 balls.
Bangladesh spinner Taijul Islam became one of the very few bowlers to take a wicket in his first ever T20 delivery on the day when he removed Brendan Taylor thanks to a Mahmudullah catch in the first ball of the second over.
Shakib had asked Zimbabwe to bat first, but they could not cope up with the Bangladesh bowling as the Tigers kept striking every now and then till Burl and Mutombodzi made a big partnership.
Opener Hamilton Masakadza, also their captain, was the odd one out, making 34 off 26 balls thanks to five fours and a six.
Mustafizur Rahman, Mohammad Saifuddin and Mosaddek Hossain claimed one wicket each.