Bangladesh left-arm spinner Taijul Islam claimed his second five-wicket haul to finish with a career-best 11-170 on Monday, but Zimbabwe stayed in a position of dominance in the first Test.
Before the bad light brought a premature end to the third day, half an hour earlier than the scheduled time, the hosts reached 26-0 after Zimbabwe set a target of 321 to win the Test.
Bangladesh's highest successful fourth-innings chase is 217-6 against the West Indies at St. George's in 2009. The hosts have won only three matches in 28 when chasing a target in the fourth innings.
Taijul, however, was instrumental in triggering a collapse in Zimbabwe's second innings, when they were bowled out for 181 from a dominating 101-2.
Taijul's 5-62, following his 6-108, was complemented by off-spinner Mehidy Hasan's 3-48 and left-arm spinner Nazmul Islam's 2-27.
Mehidy broke through by dismissing opener Brain Chari for 4 to give the hosts hope in the morning session when Zimbabwe began the day on 1-0. But Brendan Taylor counterattacked in a bid to keep Bangladesh's spinners at bay.
Islam ended Taylor's attacking knock by inducing him to play a big shot, resulting a catch at long-on. Taylor scored 24 off 25, hitting four boundaries.
Mehidy, however, got the prized wicket of Hamilton Masakadza for 48, ending his 104 ball knock. Taijul then took three wickets in five balls to raise the prospect of bowling Zimbabwe out cheaply.
But the resistance came from Regis Chakabva (20) and Wellington Masakadza (17), who played 116 balls between them to add 35 runs for the sixth wicket.
Bangladesh was bowled out for 143 in the first innings, its seventh straight test innings below 200, in reply to Zimbabwe's 282.