Zimbabwe struggled to chase the target, with no batsman scoring more than Ryan Burl's 29.
Bangladesh's spinners Mahedi and Rishad wreaked havoc on Zimbabwe's batting order, taking seven wickets between them and giving away just 50 runs in their combined 46 deliveries.
Mahedi, who opened the bowling, started poorly before dismissing Tadiwanashe Marumani.
In his 2nd over, he dismissed Dion Myers. In the 10th over, he completed his three-fer by getting Clive Madande.
Meanwhile, Rishad picked one wicket in each of his 4 overs. He dismissed Sikandar Raza, Milton Shumba, Burl and Blessing Muzarabani.
