Batting first after losing the toss, the tourists made 186-5 thanks mainly to a 120-run first-wicket partnership between Tanzid Hasan (58) and Saif Hassan (55).
Zimbabwe were all out for 152 with two balls remaining. The Bangladesh victory levelled the three-match series, which will be decided on Sunday in Bulawayo.
Hassan was first to fall. His attempted sweep off a delivery from Zimbabwe captain Sikandar Raza upended the leg stump.
Hasan followed his opening partner to the pavilion just four deliveries later. His inside edge off Richard Ngarava was deflected on to the leg stump.
Hassan struck a six and eight fours from 45 balls at Queens Sports Club and Hasan two sixes and six fours from 44.
Ngarava (2-23) and Brad Evans (2-65) were most successful in a seven-man Zimbabwe attack.
Zimbabwe made a disastrous start in reply, slumping to 21-3 with Mahedi Hasan (3-24) dismissing opener Tadiwanashe Marumani (four) and Dion Myers (four) cheaply.
Staring a heavy defeat at 108-8, tailenders Brad Evans (25) and unbeaten Ngarava (15) put on 40 runs for the ninth wicket.
Ryan Burl top scored for the hosts. His 29-run knock included a six and a four, He departed after a pull shot off Rishad Hossain (4-26) was caught by Parvez Hossain Emon at deep mid wicket.
Zimbabwe are seeking an all-formats treble against Bangladesh. After winning a one-off Test, they were 2-1 victors in an ODI series.
– AFP
Photo: Zimbabwe Cricket
