Bangladesh fought back to reduce Zimbabwe to 92 for four at stumps on Sunday on the third day of the one-off Test.
"To get Zimbabwe's top four batsmen was fantastic," Stuart Law, the Bangladesh coach, said.
Zimbabwe lead overall by 175 runs with six second-innings wickets left. The hosts started with an 83-run first innings lead by earlier dismissing Bangladesh for 287, with pace bowler Brian Vitori finishing with figures of four for 66 on his debut.
Alan Butcher, the Zimbabwe coach, dismissed suggestions that Bangladesh were now in control.
"I wouldn't say that," Butcher said. "Our top order got themselves out rather than Bangladesh getting them out."