Bangladesh lost Shamsur Rahman (two) in the first over of the second and last T20 after they won the toss and opted to bat first at the Queens Sports Club in Bulawayo.
Tamim Iqbal and Shakib al Hasan, however, added 82 runs in just 8.1 overs to take control of the match.
Shakib made 40 off 28 with six fours and a six before being caught at deep square-leg off leg-spinner Natsai Mushangwe. Tamim struck the same number of fours and sixes as his partner, before departing for 43 from 30 balls.
Bangladesh looked to be heading for a large totalbut their progress was checked by poor shot selection. The dismissals of Mushfiqur Rahim (17), Nasir Hossain (27), Mahmudullah (one) and Mominul (nine) brought the home side back into the game.
Abdur Razzak (6* off six) and SohagGazi (8* off seven) tried to improvise in the dying overs, but failed to get bat on ball for the most part.
