Shakib Al Hasan and MushfiqurRahim scored half centuries but Brian Vitori's five-wicket haul proved too much for the visitors, who were dismissed for 184 in the first ODI at Harare on Friday.
Earlier, Zimbabwe captain Brendan Taylor won the toss and sent Bangladesh in to bat in the series-opening limited-overs international at the Harare Sports Club on Friday.
Zimbabwe made two changes from the side which won the one-off Test match Monday in a victorious return to the five-day format. Batsman Foster Mutizwa and spinner Prosper Utseya come in for opening batsman TinoMawoyo and pace bowler Kyle Jarvis.
Jarvis took five wickets on debut in Zimbabwe's 130-run win on Monday, its first Test victory in seven years.
Zimbabwe hadn't played a Test since late 2005, and hadn't won in the format since beating Bangladesh at the same ground in February 2004.
Taylor is on a high after scoring 71 and 105 not out in his first test to provide the backbone of batting for the hosts. Zimbabwe continued to play in ODI cricket during its absence from the test arena and expects to be competitive against Bangladesh in the 50-over format.
