Bangladesh now need eight more wickets to level the series 1-1 as the visitors reached 76/2 at stumps on day four, with opening batsmen Hamilton Masakadza (25) and Brian Chari (43) were dismissed in the final session.
In Bangladesh’s innings, right handed batsman Mahmudullah scored 101 off 122 smashing 4 fours and 2 sixes at Shere Bangla National Stadium, Dhaka.
Masakadza’s Zimbabwe bowled out for 304 at stumps the previous evening in reply to the hosts' 522/7 declared in the first innings.
Mahmudullah's ton and Mohammad Mithun's 67 helped Bangladesh declare their second innings on 224/6. This is his first Test hundred since 2010.
The Tigers have set Zimbabwe a daunting target of 443 to win the second Test in Mirpur today.
Earlier, Musfiqur Rahim went past Shakib Al Hasan to become to record holder for the highest individual innings by a Bangladesh batsman with his unbeaten 219.
Rahim is now the first keeper to score two double-hundreds in Test history. Rahim scored unbeaten 219 off 421 balls smashing 18 fours and 1 six with Bangladesh declared their innings at 522.