Australia closed the third day on 161/4, still 67 runs short of Bangladesh's total, with six wickets in hand. The Tigers will look to make an early breakthrough on Sunday, knowing the remaining Australian batters must first overcome that deficit before they can establish a defendable lead.
Hasan Mahmud again proved Bangladesh's chief threat with the new ball. After recording 6/55 in Australia's first innings, the paceman removed both openers in the second innings, bowling Jake Weatherald for a duck before sending Travis Head back for 17.
Marnus Labuschagne then made 31 alongside Steve Smith, whose 44 helped the pair stem the flow of wickets and rebuild the innings.
Taijul Islam eventually broke up the partnership by dismissing Labuschagne, while Mehidy Hasan Miraz accounted for Smith. Cameron Green and wicketkeeper Alex Carey subsequently held firm as Bangladesh maintained pressure through accurate, testing spells.
Earlier, Bangladesh's lower order had pushed their advantage beyond 200, with Miraz's determined 65 playing a major role.
Australia paceman Josh Hazlewood stood out despite fielding lapses, taking 6/89 and claiming Bangladesh's final wickets, including Miraz.
His haul also took him to 300 Test wickets, making him the ninth Australian to reach the landmark and joining Mitchell Starc, Nathan Lyon and Pat Cummins in the country's elite club.
Joe Root has admitted he is "really hacked off" by Brydon Carse's latest off-field controversy, insisting England must rebuild trust after the fast bowler was withdrawn from the squad for the second Test against Pakistan.
England fast bowler Brydon Carse has been withdrawn from the squad for the second Test against Pakistan after an incident at a nightclub sparked an investigation by the Cricket Regulator.
Dhruv Jurel struck the second Test century of his career as India strengthened their grip on the second Test against Sri Lanka.
Pat Cummins has welcomed Australia's long-awaited return to South Africa, describing the Proteas as a "really strong side" as the visitors begin preparations for a three-Test series in October.
