The Aussies scored the required 157 runs with 9 balls to spare.
Earlier, Australian skipper Steven Smith had won the coin toss and decided to field first.
Bangladesh managed a decent 156 runs for the loss of 5 wickets but failed failed to score at a brisk pace in the first half of their innings.
The men in green also lost their opening wicket for 2 runs.
However a late surge from Mahmudullah Riyad, who remained unbeaten at 49 brought some momentum in their innings.
He's 29-ball innings consisted of 7 fours and a six.
Shakib Al Hasan too performed well with the bat as the former Bangladeshi skipper chipped in with 33 runs.
For Australia, Adam Zampa was the pick of the bowlers, picking up 3 wickets. Shane Watson chipped in with 2 wickets.
Starting the chase, the Australian openers made light of the work as they posted a decent 62 runs for the opening wicket.
After Shane Watson was run out for 21 runs, his fellow opener Usman Khwaja batted well and scored his maiden half century in T20I.
Khwaja scored 58 runs off 45 balls with the help of 7 fours and a six.
Other significant contributions were made by David Warner (17 off 9 balls) and Glenn Maxwell (26 off 15 balls).
For Bangladesh, Al Hasan picked up 3 wickets, followed by Mustafizur Rahman's brace and a solitary scalp by Al-Amin Hossain.
Adam Zampa was adjudged the man of the match.
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