Left-arm spinner Taijul Islam became the first bowler to claim a hat trick in his limited-overs international debut as Bangladesh took just 30 overs to dismiss Zimbabwe for 128 in the fifth and final ODI.
Islam had figures of 4-11, while Shakib Al Hasan (3-30) and Jubair Hossain (3-30) pitched in to dismantle the Zimbabwe batting lineup.
In reply, the hosts survived jitters to reach the target in the 25th over for the loss of five wickets.
Mahmudullah top-scored with an unbeaten 51.
Hamilton Masakadaza top scored for Zimbabwe with 52 and Vusi Sibanda made 37. No other Zimbabwe batsmen could reach double figures after the visitors won the toss and elected to bat.