Bangladesh captain Mashrafe Mortaza conceded Australia's superior performance with the bat in the opening six overs was the difference in their three-wicket World Twenty20 loss on Monday.
Having been put into bat in Bangalore, Bangladesh reached 156-5 thanks in part to Mahmudullah's unbeaten 49 off 29 deliveries.
However, Usman Khawaja's maiden T20I half-century helped seal victory for Australia, who ended the powerplay on 51-0 in contrast to Bangladesh's 33-2 at the same stage.
Bangaldesh did a decent job with the ball in their efforts to save the game but were unable to prevent Australia from sealing a victory that keeps their semi-final hopes intact.
While Australia still have a chance to progress, Bangaldesh - who started the Super 10 stage with a loss to Pakistan - have a mountain to climb ahead of contests with India and New Zealand.
"First six overs was crucial, we knew this ground was high-scoring," Mashrafe said.
"Our fielding and bowling could have been better. Mahmudullah played really well, [Mohammad] Mithun and Shakib [Al Hasan] too.
"Two losses in a row, but we have two matches left and we'll see what happens."