Bangladesh break through after Taylor's counter-attack
Bangladesh will look to take seven more wickets while Zimbabwe will target another 337 runs on the final day of the Harare Test tomorrow.
Zimbabwe, chasing a victory target of 477 runs, were 140 for three in their second innings when stumps were drawn on the fourth day.
After Bangladesh had declared their second innings on 284 for one shortly before Tea, it had seemed like the visitors were on the top and the hosts might crumble in face of Bangladesh's spinners as well as the scoreboard pressure.
But credit to Zimbabwe captain Brendan Taylor who took the attack to the opposition with some fearless cricket. His 73-ball 92 helped the hosts reach a decent total and make them dream of at least a draw on the final day.
The other opener, Milton Shumba, had fallen to Taskin Ahmed for 11 while Taylor's blitzkrieg ended courtesy of a caught-and-bowled by Mehedi Hasan Miraz.
Takudzwanashe Kaitano was the last man to fall, shortly before close of play, for a 102-ball seven. His patient knock came to an end when umpire Marais Erasmus adjudged him leg-before against Shakib Al Hasan on a delivery which looked headed down the leg stump.
Dion Myers was not out on 17 with nightwatchman Donald Tiripano batting on seven.