Chittagong: Bangladesh need a further 33 runs with two wickets left for a maiden Test victory over England after closing day four on 253-8 in Chittagong.
England's final two wickets lasted barely four overs and the tourists added only 12 runs as they were all out for 240, leaving the hosts chasing 286.
Imrul Kayes hit a fast 43 and Mushfiqur Rahim (39) put on 87 with debutant Sabbir Rahman as they reached 227-5.
Gareth Batty took 3-65 but Sabbir, dropped on 34, remains unbeaten on 59.
Bangladesh have won only seven of their previous 93 Tests, losing all eight matches against England to date.
Brief scores
England - 293 (Moeen 68, Bairstow 52, Mehedi 6-80) and 240 (Stokes 85, Shakib 5-85)
Bangladesh - 248 (Tamim 78, Stokes 4-26, Ali 3-75) and 253 for 8 (Sabbir 59*, Batty 3-65)
Status - Bangladesh to 33 runs to win