Bangladesh defeated Austria by five wickets in Wednesday's second Twenty20 International and took a 2-0 lead in the five-match series.
Mustafizur Rahman troubled the Aussies with his pace bowling and then Atif Hossain shone with the bat to guide the hosts to victory.
Atif struck five boundaries and a six in his unbeaten 37, which helped Bangladesh chase 122 after they were 67-5 following 11.2 overs.
Wicketkeeper Nurul Hasan (22 not out) partnered Atif in rescuing the hosts after they had a rocky start in Dhaka.
Earlier, Mustafizur took 3-23 and Shoriful Islam bagged 2-27 as Bangladesh's fast bowlers restricted Australia to 121-7, with Mitchell Marsh (45) top-scoring for the visitors after they won the toss and elected to bat.
Bangladesh won the opening match on Tuesday by 23 runs, claiming their maiden T20 victory over Australia.
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