Bangladesh made it two dominant days out of two in Darwin, with Tanzid Hasan Tamim's maiden Test century setting up a first-innings lead that had swelled to 153 by the close, leaving Australia staring at a mountain to climb in the first Test.
Resuming on 96 for 1, Bangladesh added freely through the morning with Tanzid and Mominul Haque taking the score past Australia's first-innings total of 198 without much alarm. Tanzid brought up his maiden Test fifty from 102 balls before lunch, having already survived a life on nought when Nathan Lyon shelled a return catch on the opening evening.
He was let off again on 62, this time by Alex Carey and Steve Smith combining unsuccessfully in the slips. Mominul fell for a well-made 49 off 95 balls, edging Josh Hazlewood behind after a 102-run stand, but by then the platform was already laid.
Tanzid went on to complete his century off 188 balls in the 64th over, stepping out to drive Lyon towards long-off before punching the air, removing his helmet and kissing the Bangladesh crest as captain Najmul Hossain Shanto led the celebrations.
It made him the first Bangladeshi batter to score a Test century on Australian soil, in only the second appearance of his career, eclipsing Hannan Sarkar's 76 at Cairns in 2003 as the country's highest individual score in the country. He fell soon after for 101 off 197 balls, holing out to Mitchell Starc off Lyon while attempting to clear long-off, an innings built on eight fours and a six.
The knock also placed the 25-year-old, against an attack featuring Pat Cummins, Starc and Hazlewood, in a select group of visiting batters to have scored Test centuries in Australia against that pace trio, a list including Virat Kohli, Babar Azam, Cheteshwar Pujara, Rishabh Pant, Ajinkya Rahane, Yashasvi Jaiswal, David Malan, Jonny Bairstow and Yasir Shah.
His dismissal ended a 92-run stand with Shanto, who continued to bat fluently and brought up his own half-century from 74 balls before going on to 84 off 127, striking seven fours and a six. The captain's dismissal, caught behind off Hazlewood, ended a 66-run partnership with Mushfiqur Rahim and brought Bangladesh's first look past 300 in a Test innings in Australia.
The second new ball then briefly threatened a slide. Litton Das edged Starc without scoring, and Mushfiqur fell for 36 to a Pat Cummins delivery that bounced extra, caught by Smith at second slip in what was the Australian's 218th Test catch, drawing him level with Joe Root for the most by a fielder in the format..
Bangladesh lost three wickets for 11 runs in the space of a few overs, the only period all day in which Australia looked capable of exerting control. Mehidy Hasan Miraz and Hasan Mahmud, fresh off his career-best six for 55 with the ball, then came together to steady the innings.
The pair batted with patience through the final session, adding their runs in singles and twos as Australia turned to Lyon and part-timer Marnus Labuschagne in search of a breakthrough. Hasan survived an lbw review off Lyon that replays showed had missed the bat entirely, while Miraz was dropped at gully off Labuschagne with the day almost done.
Their unbroken stand carried Bangladesh from 312 for 6 to 351 for 6 at the close, with Hasan unbeaten on 13 and Miraz not out on 32.
History offers Australia a sliver of hope in this position: two decades ago in Fatullah, they hauled themselves back from a similarly steep first-innings hole against Bangladesh to snatch victory. But the sides that met that day bear little resemblance to these two, with Bangladesh now a far more complete outfit and Australia short of the aura that defined their golden generation.
Bangladesh will resume tomorrow with both the runway and the belief to push the lead out further, and few would bet against them doing exactly that. Even so, nothing is settled with three days still to play.