Bangladesh fans turned up with flags and banners, some thanking the Australian team for making the series happen.
In overcast conditions, Pat Cummins snatched the early toss advantage away from Bangladesh by dismantling the top-order for just 10 runs.
Shakib Al Hasan, playing in his 50th Test, came to Bangladesh's rescue with a counter-attacking display of batsmanship.
Tamim Iqbal was dogged for most parts, except while hitting Nathan Lyon for two glorious sixes - one straight down the track and the other over deep cover.
Shakib and Tamim Iqbal brought up their half-centuries in the post-Lunch session
Against the run of play, Glenn Maxwell broke through, dismissing Tamim Iqbal for 71.
Nathan Lyon finally found a breakthrough, dismissing Shakib Al Hasan for 84.
A rain break arrived shortly, keeping the players off the field for a brief period.
Ashton Agar capped his Test return after four years with wickets of Mushfiqur Rahim, Nasir Hossain and Shafiul Islam
After bowling out Bangladesh for 260, Australia couldn't consolidate as they suffered a shaky start
Mehedi Hasan and Shakib combined to reduce Australia to 18 for 3 at stumps.