Bangladesh remained in control of the Darwin Test after Australia reached 161 for four at the end of the third day, still trailing by 67 runs with six wickets in hand.
Bangladesh, who had taken a commanding 228-run first-innings lead after being bowled out for 426 in reply to Australia's 198, reduced the hosts to 161 for four in their second innings at Marrara Stadium.
Resuming the day on 351 for six, Bangladesh added 75 runs before being bowled out for 426. Mehedi Hasan Miraz top-scored with 65, while Taskin Ahmed remained unbeaten on 14.
Australia's Josh Hazlewood was the standout bowler, finishing with six wickets for 89 runs. His dismissal of Miraz also completed his 300th Test wicket, making him only the ninth bowler to reach the milestone in Test cricket.
Hasan Mahmud, who claimed six wickets in Australia's first innings, made an immediate impact again with the ball. He bowled opener Jake Weatherald without scoring before removing Travis Head for 17.
Marnus Labuschagne and Steven Smith then added 36 runs before Taijul Islam bowled Labuschagne for 31. Smith looked settled but was dismissed for 44 by Miraz, who took a return catch to give Bangladesh their fourth breakthrough.
Australia were reduced to 122 for four, but Cameron Green and Alex Carey steadied the innings. The pair put together an unbeaten 39-run partnership from 94 balls to take Australia safely to stumps.
Green was unbeaten on 43, while Carey was 19 not out.
Earlier, Hasan Mahmud was dismissed for 14 after facing 92 balls, ending a 46-run seventh-wicket partnership with Miraz. Taijul Islam contributed a brisk 17 off 23 balls before falling to Hazlewood.
Miraz reached his 10th Test half-century and added 46 runs with Taskin before being caught behind by Alex Carey off Hazlewood.
Bangladesh's 426 is their second-highest Test total against Australia, behind the 427 they scored in the first innings of the 2006 Fatullah Test.
At the close of the third day, Bangladesh remain firmly in the driver's seat, with Australia still needing 67 runs simply to erase the deficit.
