Australia remain 67 runs behind, with Cameron Green unbeaten on 43 and Alex Carey on 19. The hosts now face the difficult task of first wiping out the deficit and then setting Bangladesh a challenging target in the final innings.

Bangladesh need six wickets to secure their first Test win in Australia and potentially their biggest victory in the format.

Resuming at 351-6, Mehidy Hasan Miraz guided Bangladesh’s lower order to another 75 runs as the visitors reached 426, stretching their first-innings lead beyond 200.

Mehidy added 46 runs with Hasan Mahmud, 18 with Taijul Islam and 46 with Taskin Ahmed before being dismissed for 65 off 154 balls.

He later returned with the ball and made the key breakthrough by removing Steve Smith late in the day.

Josh Hazlewood claimed all four wickets to fall on Saturday and finished with 6-89 from 28 overs.

His fifth wicket of Mehidy was also his 300th Test wicket, making him the fourth member of Australia’s “Big Four” bowling attack to reach the milestone and the ninth Australian overall.

Hazlewood then dismissed Ebadot Hossein, caught behind for 7, to bring Bangladesh’s innings to an end at 426.

Australia’s biggest first-innings deficit overcome to win a home Test is 206 runs. They achieved that against Pakistan at the Sydney Cricket Ground in 2010.

With Bangladesh needing just six more wickets, Australia have a huge task ahead if they are to avoid a historic defeat.

The two-Test “Top End” series is also the start of a demanding 12-month schedule for Australia, which includes 20 Test matches and tours of South Africa, India and England.