Steve Smith was bowled for eight inside the first 15 minutes of day two as Australia's first Test predicament went from bad to worse in Dhaka.
Bangladesh spinner Mehedi Hasan knocked over an advancing Smith, the Aussie skipper looking to whip the ball through a vacant midwicket.
The skipper's wicket reduced the score to 4-33 after the visitors went to stumps on day one at 3-18, having earlier bowled out Bangladesh for 260 with a disciplined performance in oppressive heat and humidity.
Opener Matt Renshaw and Peter Handscomb were the not out batsmen.
After stumps on day one, Nathan Lyon, who overtook Richie Benaud as the second-highest spin wicket-taker in Australian history on the way to snaring his 250th Test wicket, declared that the game remained in the balance.
"It's not ideal losing three wickets but that's the game," Lyon said on Sunday.
"You've got to give them credit, they batted well, they bowled well. Now it's our chance to fight back and really test ourselves in these conditions.
"We've got two very, very good batsmen (at the crease) ... we're just going to have to work hard, bat well and bat long in partnerships.
"There's no demons in that pitch as yet so it's a good opportunity for our batters."
Bangladesh squad: Mushfiqur Rahim (c), Tamim Iqbal, Soumya Sarkar, Imrul Kayes, Shakib Al Hasan, Mehidy Hasan Miraz, Sabbir Rahman, Nasir Hossain, Liton Das, Taskin Ahmed, Shafiul Islam, Mustafizur Rahman, Taijul Islam, Mominul Haque.
Australia squad: Steve Smith (c), David Warner (vc), Ashton Agar, Jackson Bird, Hilton Cartwright, Pat Cummins, Peter Handscomb, Josh Hazlewood, Usman Khawaja, Nathan Lyon, Glenn Maxwell, Matthew Renshaw, Mitchell Swepson, Matthew Wade.