Australia were bowled out for 198 in 53 overs, with Hasan returning career-best Test figures of 6 for 55.
Taskin Ahmed and Ebadot Hossain claimed two wickets apiece as Bangladesh’s pace attack dismantled Australia’s batting line-up.
Steven Smith offered the most resistance for the hosts, scoring a patient 71 off 109 balls with seven fours and a six.
However, Hasan removed Smith late in the innings to complete his six-wicket haul, before Nathan Lyon fell to the same bowler to wrap up the Australian innings.
In reply, Bangladesh made an encouraging start, reaching 96 for 1 in 24 overs at stumps. Tanzid Hasan remained unbeaten on 32, while Mominul Haque was also not out on 35.
The pair added an unbroken 60-run stand after Shadman Islam was dismissed for 20 by Mitchell Starc.
Bangladesh still trail by 102 runs, but their disciplined bowling effort and confident batting response have put them firmly in control after the opening day.
With nine wickets in hand and the experienced Najmul Hossain Shanto, Mushfiqur Rahim and Litton Das still to come, Bangladesh will look to go on top in Test opener.
