Rajin Saleh (65) and Mohammad Rafique (five) were the not out batsmen at the break on Monday after the home side crossed the 400-run mark in a Test innings for only the fourth time since gaining Test status in 2000.
Resuming at 355-5, Bangladesh's overnight pair of Saleh and Khaled Mashud (17) saw off the threat of the second new ball, careful not to play the deliveries outside the off stump.
Saleh scored just 30 runs in the session but completed a useful fifth half-century in 16 Tests.
The 22-year-old was lucky to survive a chance on 48 when paceman Jason Gillespie dropped an easy return catch but continued to bat cautiously.
Saleh had so far faced 192 balls and hit six fours.
Mashud, who batted 105 minutes, became Stuart MacGill's fourth victim when the leg-spinner had him stumped by Adam Gilchrist.
This is the first match of a two-Test series. The second Test will be held in Chittagong from April 16.