Zimbabwe reached 138-4 in pursuit of a victory target of 401 by stumps on day four of the second Test against Bangladesh in Harare.
Shakib Al Hasan (2-45) and Ziaur Rahman (2-36) each claimed two wickets to put the tourists in a strong position to push for a victory on the final day that would earn them a share of the two-match series.
Zimbabwe need a further 263 runs and their hopes rest with Hamilton Masakadza, who closed on 46 not out alongside his brother and nightwatchman Shingi (7no).
Bangladesh had earlier extended their second innings from 163-5 at the start of day four to a mid-afternoon declaration at 291-9.
Skipper Mushfiqur Rahim top scored with 93, while Nasir Hossain's 67 not out was his second half-century of the match.
The Masakadza brothers were Zimbabwe's most successful bowlers. Paceman Shingi took 4-58, while Hamilton picked up a career-best 3-24 with his occasional seamers.