Tigers scored 45 runs for 1 wicket after 22 overs in their 2nd innings of first Test at the end of Day 2 at the Sher-e- Bangla National Cricket Stadium on Monday.
Bangladesh now ahead of 88 runs with 9 wickets remaining in their hand.
Soumya Sarkar was caught out once again at the previous over of the last over of the day.
Tigers have assumed control of this Test, leading by 88 with nine wickets in hand on a pitch that is turning, bouncing and seaming around
Tamim played steadily from the beginning of the innings and scored 30 runs off 70 balls. He was accompanied by Taijul Islam with 0 runs.
Taijul was sent to the crease as the night watchman.
In their first innings, Australia were all out for 217 in their first innings, conceding a 43-run lead to Bangladesh.
Australian opener Matt Renshaw (45) was the top scorer for Australia, while left-arm spinner Shakib Al Hasan was the pick of the Bangladesh bowlers with figures of 5-68.
That was Shakib AL Hasan's 16th five-wicket haul in Tests.