Opting to bat first, Zimbabwe lost Sharne Mayers on the first ball of the innings, trying to pull Jahanara Alam. Ashley Ndriya got out for a three-ball duck in the next over to Salma Khatun.
Modester Mupachikwa scored 33 runs from 51 balls, while skipper Mary-Anne Musonda and Loreen Tshuma got out in quick succession.
Precious Marange, Esther Mbofana, Audrey Mazvishaya and Francisca Chipare did not last long as Nahida Akter and Fahima Khatun ran through the lower order.
Nyasha Gwanzura remained unbeaten till the end, scoring 35 runs from 80 balls. Zimbabwe were all out for 121 in 46.4 overs. Nahida Akter was the pick of the bowler, taking three wickets for 30 runs.
In the chase, Bangladesh lost Sharmin Akhter early, but Murshida and Hoque made sure that the tourists did not lose further wickets. Khatun scored 51 runs from 65 balls while Hoque made a 68-ball 53.
Zimbabwe 121 all out 46.4 overs (Nyasha Gwanzura 35*; Nahida Akter 3/30) lost to Bangladesh 125/1 in 24.3 overs (Fargana Hoque 53*; Esther Mbofana 1/30) by 9 wickets.