Bangladesh were 45-1 at stumps in their second innings after they bowled out Australia for 217 on day two of the opening Test in Dhaka on Monday.
Tamim Iqbal was on 30 with nightwatchman Taijul Islam (0) after Ashton Agar dismissed Soumya Sarkar for 15.
Earlier, spinners Shakib Al Hasan (5-68) and Mehedi Hasan (3-62) helped Bangladesh claim a 43-run first innings lead.
Matt Renshaw top-scored with 45 and Agar hit an unbeaten 41.
