Opener Shahriaf Nafees was batting on a sparkling 60 and captain Habibul Bashar was on 45 after the home side elected to bat on Sunday.
Left-handed Nafees had so far struck 10 fours off 67 balls and Bashar eight off 47. The pair had added 93 runs for the unbroken second wicket stand.
The home side raced to 100 in the 20th over with Nafees playing fine shots all over the ground and Bashar joining him in the run feast.
Nafees had earlier put on 51 with opener Javed Omar (27), who was trapped leg-before by paceman Jason Gillespie.
Omar struck six fours including two consecutive ones down the leg side off new-ball bowler Stuart Clark.
The second and final Test will be held in Chittagong from April 16.
Bangladesh have lost both their previous Tests to Australia by innings margins.