Pat Cummins, Nathan Lyon and Ashton Agar took three wickets each to wrap up the Bangladesh innings despite half-centuries from Tamim Iqbal and Shakib al Hasan.
But there was redemption for Bangladesh -- meeting Australia in a Test for the first time in over a decade -- when their spinners took two scalps in the final moments of the session. A third batsman was run out, leaving Australia precariously placed on 18-3 at stumps.
David Warner was given a reprieve by the third umpire from a lbw decision off Mehedi Hasan, but the spinner trapped the left-hander the same way with the very next ball.
Soumya Sarkar was responsible for a brilliant run out to remove Usman Khawaja for one in the next over, before left arm spinner Shakib Al Hasan dismissed nightwatchman Lyon for a duck.
Opener Mat Renshaw remained unbeaten on six at stumps along with skipper Steve Smith, not out three.
When the match got under way Australia looked unstoppable as Cummins rattled Bangladesh’s top order with a fiery opening spell.
Cummins struck in his first over when he dismissed Soumya Sarkar for eight, beating the left-hander with a short-pitched ball that took an edge and flew to Peter Handscomb at gully.
In his next over he removed Imrul Kayes and Sabbir Rahman for nought off successive deliveries to reduce Bangladesh to 10 for 3.
But Shakib and Tamim came together to add 155 for the fourth wicket and lift the home team's score towards respectability.
Tamim lofted Lyon for a six over extra cover, growing in confidence as he built the partnership with Shakib.
Occasional spinner Glenn Maxwell finally broke it when he forced Tamim to cut one loose at backward point, where David Warner took the catch.
Tamim, who like Shakib was playing his 50th Test, made 71.
Shakib scored 84 including 11 fours before he was dismissed by Lyon on the stroke of tea, with Smith taking a sharp catch at first slip.
“It was quite challenging to bat out there. I think Tamim and I applied ourselves,” said Shakib.
“It was an important partnership. We may be in the driving seat but we need to take seven more wickets.
“They have some batting left too, so we have to focus well. Every day gives you a new situation in Test cricket,” he added.
Agar trapped Mushfiqur Rahim leg-before for 18, a decision which the Bangladesh skipper unsuccessfully reviewed.
Nasir Hossain (23) and Mehedi Hasan (18) provided brief resistance but were undone by Agar and Lyon respectively for Australia to expose the tail.
Cummins finished with figures of 3-63, while off-spinner Lyon claimed 3-79 -- surpassing Richie Benaud's Test haul of 248 wickets to become Australia's second most successful spinner after Shane Warne.
“It's in the balance to be fair,” Lyon said after the opening day’s play.
“You can probably look at Bangladesh who have the momentum at the moment. To lose the toss and bowl a team out for 260 or under 300 is always a good result for a bowling team.
“It's not ideal losing three wickets, but that’s the game. You’ve got to give them credit, they batted well, they bowled well,” he said.
Agar, playing his first Test in four years, did his part with 3-46 which included the final wicket of Shafiul Islam.
Australia vs Bangladeshaustralia vs bangladesh 2017Bangladesh vs Australia 2017Mehedi HasanMirpur TestNathan Lyonshakib al hasan
First Published: August 27, 2017, 7:21 PM IST