Bangladesh reduced Zimbabwe to 76/2 Wednesday on the fourth day of the second Test. The visitors still needs 367 runs or to survive a full day to win its first Test series victory since 2011 after the hosts set an improbable target of 443 runs.
Bangladesh skipper Mahmudullah was instrumental in leaving Zimbabwe a record chase, hitting his second century as the hosts declared the second innings on 224/6.
Mahmudullah, who completed his century in the last ball before the tea session, was not out on 101 and shared two important partnerships to take the side on the verge of winning the Test and drawing the series.
Bangladesh lost the first Test by 151 runs.
"We just need to bowl in right line and length and then it will be easier for us," Bangladesh offspinner Mehidy Hasan said. "Chasing 450 runs (443) is not easy whatever the condition is. We know they have the batsmen to block and block all day long but if we are disciplined, it's our match."
Despite a lead of 218 runs, dismissing Zimbabwe for 304 in its first innings on Day 3, Bangladesh decided not to enforce the follow-on.
But Zimbabwe fast bowlers Kyle Jarvis (2/27) and Donald Tiripano (2/31) rocked the top order to leave the hosts at 25/4.
Jarvis swung the ball in admirable fashion to remove openers Imrul Kyaes (3) and Liton Das (9) in three deliveries in the fifth over of the day.
Tiripano, who shared the new ball in the absence of injured Tendai Chatara, was equally impressive, and Mominul Haque (1) and Mushfiqur Rahim (7), the centurion and the double centurion of the first innings, perished to loose shots.
With Zimbabwe raising the hopes to hit back, Mithun and Mahmudullah resisted further damage to keep the side on course for a sizeable lead.
The duo combined for a 118-run partnership for the fifth wicket to restore its dominance.
Offspinner Sikandar Raza removed Mithun for 67, his maiden fifty in his maiden Test following zero in the first innings.
Left-arm spinner Sean Williams dismissed Ariful Haque (4) cheaply but Mahmudullah and Hasan (27 not out) shared 73 off 70 balls in an unbroken seventh wicket partnership to set an improbable target for the visitors.
Zimbabwe's highest successful chase in the fourth innings is 162 against Pakistan in Peshawar in 1998.
"The first hour will be very key," Zimbabwe coach Lalchand Rajput said. "If Brendan (Taylor) and Sean Williams can bat through, then the pressure will be on the fielding side.
"Cricket is a game of uncertainties. You never know what will happen. It just takes one or two big partnerships. It's happened. If you look at the earlier games like Pakistan-Australia, they really saved a Test match."
The tourists made a decent start with skipper Hamilton Masakadza and Brian Chari sharing 68 runs.
Hasan (1/16) gave Bangladesh the first breakthrough after Masakadza spooned a catch at short-leg for 25.
Two overs later, left-arm spinner Taijul Islam (1/34) dismissed Brian Chari (43), who tried to paddle sweep against a turning delivery. Chari reviewed in vain.
Brendan Taylor (4) and Sean Williams (2) were batting before the fourth day's game came to an end.
(With AP Inputs)