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.
Australia head coach Andrew McDonald admits Marnus Labuschagne "needs some big runs" to retain his place in the Test team as the hosts mull changes following a shock defeat Bangladesh.
India ended the second day of the first Test against Sri Lanka in complete control at 460/9 in their first innings.
Bangladesh trounced hosts Australia by nine wickets in the opening Test to create their own piece of history in Darwin on Sunday.
Opening batter Tanzid Hasan's maiden Test century made history in Australia as Bangladesh finished day two of the opening Test in a dominant position in Darwin on Friday.
