The hosts beat Steve Smith's men by 20 runs in a thrilling victory on home soil, their first ever win against Australia since gaining Test status in 2000.
Mushfiqur Rahim's men are hoping to seal the series when they square off against Australia in the second and final Test starting at Chittagong on September 4.
Australia – who are touring Bangladesh for the first time in more than a decade – are currently ranked fourth to Bangladesh's lowly ninth in ICC Test rankings.
The Baggy Greens on Wednesday added left-arm slow bowler Steve O'Keefe to their squad for the second Test. O'Keefe will replace fast bowler Josh Hazlewood who has been ruled out of the series with injury.
Mushfiqur Rahim (capt), Tamim Iqbal, Soumya Sarkar, Imrul Kayes, Shakib Al Hasan, Nasir Hossain, Sabbir Rahman, Mehedi Hasan, Shafiul Islam, Taijul Islam, Mustafizur Rahman, Mominul Haque, Liton Das, Taskin Ahmed.