The hosts notched up a competitive 167-3 after opting to bat first and a disciplined bowling display then restricted Zimbabwe to 125-8.
Sabbir Rahman was key to Bangladesh's victory with a brilliant all-round performance. He first hit an unbeaten 43 and then claimed 3-11 off 2.1 overs to rattle Zimbabwe.
Opener Soumya Sarkar also contributed 43 to give his side a fluent start. Shakib Al Hasan added 27 not out.
Soumya and Tamim Iqbal combined for 45 runs in six overs in a boundary-filled start for Bangladesh but Tamim, who scored 23 off 17 balls, was dismissed before the first powerplay ended after a top edge off a slower delivery from Taurai Muzurabani.
Zimbabwe started well but Bangladesh's bowlers hit back to stall progress.
Opener Hamilton Masakadza resisted with 30 while Malcolm Waller made 29.
Bangladesh leads the series 2-0.
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