Bangladesh won the toss and sent Zimbabwe in to bat in the third and final limited-overs international at Dhaka's Sher-e-Bangla Stadium on Friday.
The game was cut to 37 overs per team after thick fog delayed the start of play by more than two hours.
Bangladesh kept the same team that won the second ODI on Wednesday, while Zimbabwe made two changes: Chris Mpofu replaced Tawanda Mupariwa while Keith Debengwa was recalled in place of Malcolm Waller.
Zimbabwe: Prosper Utseya (captain), Hamilton Masakadza, Tatenda Taibu, Ray Price, Sean Williams, Stuart Matsikenyeri, Elton Chigumbura, Chris Mpofu, Vusi Sibanda, Ed Rainsford, Keith Debengwa.
Bangladesh: Mohammad Ashraful (captain), Mashrafe bin Mortaza, Tamim Iqbal, Mehrab Hossain, Raqibul Hasan, Shakib Al Hasan, Naeem Islam, Mahmudullah Riyad, Mushfiqur Rahim, Nazmul Hossain, Rubel Hossain.
Umpires: Zameer Haider, Pakistan and Enamul Hoque, Bangladesh.