Mirpur: As Bangladesh had been lifted out of a hole in the afternoon, so Zimbabwe were revived from a top-order collapse with an excellent partnership that gave them a 1-0 lead in the series.
Abdur Razzak's comeback to the Bangladesh XI began with three wickets in his first over, as Zimbabwe squandered a steady start, but a quick and almost effortless 99-run alliance between Elton Chigumbura and Stuart Matsikenyeri steered Zimbabwe out of a mess and on to an ultimately comfortable win.
Chamu Chibhabha had begun Zimbabwe's chase coolly, hitting some imperious shots against the new-ball bowlers, but was struck on the pads by Razzak's second ball was on his way for 26. The very next ball Brendan Taylor suffered a similar fate when he was hit in front of middle and leg.
Suddenly, Zimbabwe were 39 for 3. That became 54 for 4 when Rubel Hossain forced Hamilton Masakadza into a loose shot outside off, and when Charles Coventry's crucial cameo 32 was snapped by Dolar Mahmud, Bangladesh were cock-a-hoop. However, Chigumbura and Matsikenyeri got the chase back on track in sensible manner.
Earlier, Rahim made 56 from 78 balls with five fours and received support from lower-order batsman Dollar Mahmud, who smashed 41 off 30, including three sixes and four boundaries.
Rahim and Mahmud put on 54 runs for the ninth wicket before Bangladesh was dismissed with more than three overs to spare.
Zimbabwe all-rounder Elton Chigumbura took 3-27 off eight overs after his captain Prosper Utseya won the toss and sent Bangladesh in to bat at Sher-e-Bangla National Stadium.
Chigumbura removed openers Junaid Siddique for 0 and Tamim Iqbal for 5 to reduce Bangladesh to 5/2 in the fourth over. He followed up 11 overs later to dismiss Mohammad Ashraful for 20.
Chamu Chibhabha claimed 2-28 and Kyle Jarvis 2-43, while Ray Price and Graeme Cremer each claimed one wicket.
Brief score
Bangladesh: 186 (Mushfiqur 57, Dolar 41) by five wickets
Zimbabwe: 189 for 5 (Chigumbura 60*, Matsikenyeri 47*)
Result: Zimbabwe won by five wickets.
MOM: Elton Chigumbura (Zimbabwe)