A combined 162 runs from Bangladesh's top three set the tone as the hosts cruised to a 1-0 series lead with a 48-run victory in Dhaka.
Liton Das and Soumya Sarkar each made a half-century as Bangladesh showed their dominance from the very start. Das and fellow opener Tamim Iqbal carried their good form from the ODI series between these two teams, in which both players made two centuries including a record 292-run stand between the pair in the third and final game of the series.
They put together another masterful partnership here, moving the score swiftly on to 92 in the 10th over before Zimbabwe finally got the breakthrough, with Wesley Madhevere, one of three debutants for the visitors, picking up the wicket after a lengthy inspection of where exactly his front foot landed by the third umpire – the ball eventually was deemed legal.
Das followed soon after, trapped leg-before by Sikandar Raza for 59, but Sarkar and Mushfiqur Rahim kept the momentum going. Mushfiqur departed for a rapid 17 from 8 balls, including two sixes, leaving captain Mahmudullah to support Sarkar.
Sarkar put the cherry on top of a fabulous batting display by smashing three sixes in Chris Mpofu's final over to surge past fifty for the second time in T20Is, ending on 62* from 32 balls. Mpofu returned the unenviable figures of 1/58 from his four overs, as Bangladesh finished on 200/3.
The reply quickly looked in trouble as Brendan Taylor, Craig Ervine and Wesley Madhevere were all dismissed inside the Powerplay, a period in which the visitors could only muster 38 runs. Sean Williams and Tinashe Kamunhukamwe struck back with a 13-ball spell in which the pair found the boundary five times, with three of those clearing the rope.
But the pair then fell to consecutive deliveries from Aminul Islam to leave Zimbabwe five down in the ninth over. Sikandar Raza and Tinotenda Mutombodzi also went for single-figure scores, and while Richmond Mutumbami managed a couple of lusty blows in his 20, he soon departed as well.
Donald Tiripano, who lit up the second ODI with a 28-ball 55* to take Zimbabwe as close as they have come to a victory so far on this tour, struck three maximums in his 20 before he edged on to his stumps from the bowling of Mohammad Saifuddin.
Carl Mumba also managed to get away a few shots before becoming the final wicket when he was caught at long-off for 25 as Zimbabwe were bowled out for 152 in 19 overs.
The second T20I takes place on Wednesday 11 March at the same venue.