In the second innings, Kyle Jarvis picked up three Bangladesh wickets to finish with match haul of seven wickets in the 1st Test.
Chasing 483 to win, Bangladesh slumped to 85 for 5 before Mohd Ashraful and Nasir Hossain combined for a brief period scoring 47 runs between them.
Mohd Ashraful top scored with 40 but was run-out in the 29th over to leave Bangladesh reeling at 132 for 6.
Bangladesh were skittled out for 147 in their second innings with Graeme Cremer picking up four wickets for just four runs in 5.2 overs. Zimbabwe won the tie by 335 runs.
Brendon Taylor got to his second hundred of the game scoring 102 off 146 balls before declaring the Zimbabwe innings at 227 for 7, setting Bangladesh a target of 483 runs to win.