Usman Khawaja's first international Twenty20 half century ensured Australia bounced back from an opening defeat to New Zealand to beat Bangladesh by three wickets in the World T20.
Bangladesh - missing Taskin Ahmed and Arafat Sunny from the attack after they were suspended from bowling - were restricted to 156-5 despite Mahmudullah hitting an unbeaten 49 runs off just 29 deliveries.
Spinner Adam Zampa was the star with the ball for Australia, taking 3-23, and his effort was backed up by that of Khawaja with the bat as the opener justified his selection ahead of Aaron Finch.
Khawaja (58) needed just 37 deliveries to blast his way to fifty and, although Bangladesh took wickets at regular intervals, his contribution and Glenn Maxwell's 15-ball 26 proved enough to get Australia over the line.
Shane Watson (2-31) did the early damage as Bangladesh laboured during the powerplay and they appeared in a very poor position on 78-4 after the impressive Zampa removed Mohammad Mithun (23) and Shuvagata Hom (13).
Mahmudullah tilted the momentum in Bangladesh's favour, the right-hander prospering even after Shakib Al Hasan (33) had departed, finding particular success with the square drive as he hit seven fours and one maximum.
His superb showing gave Bangladesh a more than decent total to defend but Australia wasted little time in getting ahead of the run rate thanks to Khawaja.
Khawaja and Watson piled on 62 runs before the latter was run out for 21. However, Khawaja continued undeterred, bringing up his 50 with a fine shot to the backward point boundary.
Steve Smith (14) was done for pace by Mustafizur Rahman (2-30) and Bangladesh continued to make inroads as Khawaja's superb stay at the crease came to an end and David Warner went for a quick-fire 17.
Yet Maxwell's two fours and pair of sixes ended any hope of a Bangladesh win, which was confirmed by James Faulkner's (5 not out) sole boundary, keeping Australia's semi-final hopes intact and leaving Bangladesh with a mountain to climb following their earlier loss to Pakistan.