Openers Aaron Finch (71) and David Warner (48) set the foundation for the victory win with a quick 98-run opening partnership while chasing a competitive 153 for five by the hosts in their last Group 2 league match at the Shere Bangla National Stadium.
Finch's blistering half-century came off 45 balls and had seven hits to the fence and four over it, while Warner’s 48 came off 35 balls and included five fours and three huge sixes.
They put together 98 runs off 11.2 overs.
The duo tore apart Bangladesh's bowling with their power hitting, and except debutant Taskin Ahmed, the other Bangladesh bowlers conceded over eight runs an over.
While Al-Amin Hossain bagged the wickets of Finch and Warner, Ahmed cleaned up Glenn Maxwell to finish with figures of one for 24 from four overs.
Cameron White was unbeaten on 18, while captain George Bailey (11 not out) finished off Australia's chase in style, clobbering Hossain for a four and six as Australia amassed 158 for three in 17.3 overs.
With both Australia and Bangladesh out of the semi-finals reckoning, the match was inconsequential.
Having lost to India, the West Indies and Pakistan in their earlier group matches, a lot of pride was at stake and both teams were desperate to finish with at least one victory.
Earlier, opting to bat, Bangladesh witnessed a wobbly start before Shakib Al-Hasan and skipper Mushfiqur Rahim shared a 112-run third-wicket partnership to take the hosts out of trouble.
Shakib scored 66 off 52 balls, with the help of five boundaries and three sixes, while Mushfiqur's 47 came off 36 deliveries and was laced with five fours and one six.
Pacer Nathan Coulter-Nile rocked Bangladesh's innings early on, dismissing both the openers -- Tamim Iqbal and Anamul Haque Bijoy -- in consecutive overs to reduce the hosts to 12 for two in 3.2 overs.
Shakib and Mushfiqur then joined hands and took the attack to the opposition, stitching a 100-plus stand off a mere 78 balls.
But both fell in search of quick runs towards the end of the innings. While Shakib was dismissed by Doug Bollinger, Mushfiqur fell to Shane Watson.
Coulter-Nile (2-17) was the pick of Australian bowlers, while Mitchell Starc (1-25), Bollinger (1-31) and Watson (1-/25) accounted for a wicket each.
Image: Australia's Aaron Finch bats during the ICC World Twenty20 match against Bangladesh.
Photograph: Scott Barbour/Getty Images
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