The hosts appeared to hold the upper hand after reaching 27 for one in reply to Zimbabwe's 240 at the end of day one.
Yet Bangladesh endured similar struggles with the bat as they were dismissed for 254, Tinashe Panyangara claiming a first Test five-wicket haul.
Zimbabwe cut their arrears down to nine runs prior to stumps, reaching five without loss from two overs to leave the first of three encounters beautifully poised.
Panyangara, who claimed the only Tigers wicket on Saturday, set the ball rolling when having Shamsur Rahman caught at mid-off for eight.
Mominul Haque and Mahmudullah found the ideal riposte, yet their 63-run alliance ended with the former being run out for 53 after fatally not dragging his bat.
Bangladesh were undermined by more dreadful running when Shakib Al Hasan (five) fell the same way, despite a despairing dive.
Mahmudullah continued to resist, only to see his stay ended on 63 when he was trapped lbw by Sikandar Raza on review.
Another poor dismissal followed, Shuvagata Hom (14) striking Tafadzwa Kamungozi straight to mid-on.
Even Mushfiqur Rahim, who had played well for 64, gave it away when pulling Panyangara to square-leg.
The tail succumbed quickly as Panyangara continued to make his mark, castling Taijul Islam (19) and Al-Amin Hossain (nine) to complete figures of 5-59 after Shahadat Hossain (nought) had become the third batsman to be run out.
Zimbabwe openers Regis Chakabva and Vusi Sibanda ensured there were no alarms before the close, setting up an enthralling third day.