Opener David Warner scored an unbeaten 88 to lead Australia's robust reply to Bangladesh's first-innings total of 305 in the second and final cricket test in Chittagong.
Smarting from their embarrassing defeat inside four days in Dhaka, Australia's top order fired up to help them reach 225-2 as the tourists, still 80 runs behind, press for a pride-salvaging victory in Chittagong.
Known for his explosive batting, Warner hit only four boundaries in his patient knock as he kept Australia on course for a handy first-innings lead which often clinches test matches in the subcontinent.
Peter Handscomb, Warner's partner in their unbroken 127-run stand, braved Bangladesh's relentless spin assault and dehydration to remain not out on 69. His fourth test fifty included five boundaries.
Earlier, Nathan Lyon claimed 7-94, his second-best figure, as Bangladesh added 52 runs to their overnight score of 253-6 before collapsing.
When Australia returned to bat, Mushfiqur took a spectacular diving catch to dismiss Matt Renshaw for four but Warner and Steve Smith raised 93 runs for the second wicket to overcome the loss.
Warner defended resolutely, letting Smith dominate their partnership, before the Australia skipper was bowled through the gate for 58 by spinner Taijul Islam. Smith hit eight boundaries in his fluent knock.
New man in Handscomb proved an able ally as Warner frustrated Bangladesh with his compact defence, scoring largely through singles and twos.
The heat and humidity took a toll on Handscomb who looked dehydrated and needed medical attention towards the end before resuming batting.
Rahim wasted a stumping opportunity when Warner, then on 73, charged out to Mehidy Hasan and missed the ball which kept low and hit the stumper's pad.
Security was tightened around the match after the Australian team bus was hit by a rock on Monday.