Mominul Haque scored his fourth Test century to leave Zimbabwe chasing a world record 449-run target to win the third and final Test against Bangladesh in Chittagong on Saturday. (Scorecard)
Mominul made an unbeaten 131 as Bangladesh, seeking a 3-0 sweep after winning the first two Tests, piled up 319-5 in their second innings before declaring in the post-tea session of the fourth day's play.
The tourists ended the day on 71-1 still needing 378 runs more with nine wickets in hand to record an improbable win.
The highest fourth innings total so far that won a Test was 418-7 by the West Indies against Australia in Antigua in 2003.
Sikandar Raza was unbeaten on 43 and Hamilton Masakadza was on 26, the pair having put on 67 for the second wicket after opener Brian Chari was leg-before to Rubel Hossain for zero.
Mominul, who was playing only his 12th Test, hit 13 fours in his 189-ball innings.
He put on 113 for the second wicket with Tamim Iqbal, who missed the chance to become the first Bangladeshi batsman to score centuries in both innings of a Test when he was bowled by Natsai M'shangwe for 65.
Tamim had made 109 runs in the first innings.
Mohammad Mahmuddulah hit 30 off 28 balls, Shakib Al Hasan made 17 and skipper Mushfiqur Rahim scored a brisk 46 off 30 balls to hasten the declaration.
The Test series between the two lowest-ranked teams will be followed by five one-day internationals.