Nathan Lyon picked up 6 wickets and effected a run out to give Australia a fighting chance in the first test in Dhaka.
Australia need 265 to win the first test at the Shere Bangla National Stadium after Bangladesh were dismissed for 221 in their second innings on Tuesday.
Opener Tamim Iqbal top scored for the hosts with 78, while off-spinner Nathan Lyon was the pick of the Australian bowlers claiming 6-82.
Bangladesh innings suffered a collapse after a good start as Lyon claimed 6 wickets and also effected a freak run out to remove home skipper Mushfiqur Rahim.
Having lost nine of their first innings wickets to spin - the other, Usman Khawaja, was run out -- Australia face a Herculean task of batting in the fourth innings on a worn-out track where some deliveries have been virtually unplayable.
Lyon dismissed nightwatchman Taijul Islam and Imrul Kayes cheaply after Bangladesh had resumed on 45-1 but Tamim Iqbal and Mushfiqur added 68 runs for the fourth wicket to stretch their lead.
Tamim celebrated his 50th test appearance by hitting his second fifty of the match, his fluent 78 including eight boundaries.
Khawaja bowled the first over after the lunch break - his first deliveries in international cricket - but it was Lyon, who dented Bangladesh after lunch.
Pat Cummins dismissed Tamim with a sharply-rising delivery before Lyon mowed down the middle order.
The off-spinner accounted for the wickets of Shakib Al Hasan and Sabbir Rahman, whose straight drive Lyon deflected onto the stumps at the non-striker's end to get Mushfiqur run out for 41.
Australia's Josh Hazlewood walked off the field with what appeared to be side strain but is unlikely to be missed much in the spin-dominated contest, having gone wicketless so far in the opening match of the two-test series.
Chittagong hosts the second and final test from September 4.
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 "Australia vs Bangladesh 1st test")
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