All of the home batsmen got starts in their second knock, but wickets at regular intervals put Bangladesh into a dominant position going into day five.
The previous six tests between the pair in Zimbabwe have resulted in five wins for the home side and a draw, leaving the tourists eyeing a piece of history on the final day.
Resuming on 163 for five, Mushfiqur Rahim put on 84 for the sixth wicket with Nasir Hossain (67 not out) as the pair took the game away from the hosts.
Shingi Masakadza was the pick of the Zimbabwe bowlers with four for 58, while his older brother Hamilton weighed in with three for 24.
Zimbabwe started their chase positively, Regis Chakabva scoring at a run a ball before he was dismissed for 22. The big wicket of Zimbabwe captain Brendan Taylor (10), who scored centuries in each innings in the first test, was a huge blow for the home team’s chances and reduced them to 96 for three.
Hamilton (46) and Shingi Masakadza (seven) will resume on Monday with the home side needing to get another 263 runs to win, or to bat out 90 overs to save the test and claim the series.
Zimbabwe won the first by 335 runs and are looking for their third home test series win. Their previous two both came against Bangladesh, in 2001 and 2004.
BANGLADESH first innings 391 (Shakib Al Hasan 81, Nasir
Hossain 77, Mushfiqur Rahman 60; E Chigumbura 3-75)
Zimbabwe first innings 282 (E Chigumbura 86; Robiul Islam
5-85, Sohag Gazi 4-59)Bangladesh second innings (163 for five overnight)
Tamim Iqbal c Mutumbami b S Masakadza 7
Jahurul Islam c Mutumbami b S Masakadza 2
Mohammad Ashraful lbw Jarvis 4
Mominul Haque c H Masakadza b S Masakadza 29
Shakib Al Hasan c Mutumbami b H Masakadza 59
Mushfiqur Rahim c Sibanda b H Masakadza 93
Nasir Hossain not out 67
Ziaur Rahman st Mutumbami b Cremer 0
Sohag Gazi c Sibanda b H Masakadza 11
Sajidul Islam c Mutumbami b S Masakadza 4
Robiul Islam not out 4
Extras (lb-5, w-2, nb-4) 11
Total (for nine wickets declared, 88 overs) 291
Fall of wickets: 1-7 2-12 3-18 4-65 5-149 6-233 7-234 8-255
9-279
Bowling: K Jarvis 22-3-80-1 (nb2), S Masakadza 24-5-58-4
(nb2), G Cremer 17-1-70-1, E Chigumbura 14-0-54-0 (w1), H
Masakadza 11-1-24-3 (w1)
ZIMBABWE second innings
V Sibanda c Sohag Gazi b Shakib Al Hasan 32
R Chakabva b Shakib Al Hasan 22
H Masakadza not out 46
B Taylor lbw Ziaur Rahman 10
M Waller b Ziaur Rahman 15
S Masakadza not out 7
Extras (lb-5, nb-1) 6
Total (for four wickets, 43.4 overs) 138
Fall of wickets: 1-36 2-66 3-96 4-118
To bat: R Mutumbami, E Chigumbura, G Cremer, K Meth, K
Jarvis
Bowling: Robiul Islam 8.4-2-24-0 (nb1), Sajidul Islam
2-1-5-0, Shakib Al Hasan 9-0-45-2, Sohag Gazi 12-5-23-0, Ziaur
Rahman 12-4-36-2.