
Chasing a target of 110, Australia reached 112 for 3 in 11 overs. Captain Mitchell Marsh led the chase with 60 runs from 28 balls, hitting seven boundaries and four sixes before being caught by Shamim Hossain off the bowling of Shoriful Islam.
Marsh and Josh Inglis put on 54 runs for the opening wicket inside the six-over powerplay.
Inglis made 17 off 16 balls before falling to Nasum Ahmed, while Cooper Connolly added 15 runs. Matt Renshaw, named player of the series, and Tim David remained unbeaten at the crease to secure the victory.
Nasum was the most economical bowler for Bangladesh, taking 1 for 10 from his three overs.
Earlier, Bangladesh won the toss, elected to bat first at the Bir Sreshtho Flight Lieutenant Matiur Rahman Stadium, and were restricted to 109 for 8 in 20 overs.
The hosts suffered a top-order collapse, falling to 11 for 3 in the fifth over as Tanzid Hasan was run out for 5, Saif Hassan fell to Spencer Johnson for 1, and Parvez Hossain Emon was caught off Nathan Ellis for 1.
Bangladesh captain Towhid Hridoy anchored the remainder of the innings, top-scoring with an unbeaten 61 from 51 balls, which included three boundaries and two sixes.
Rishad Hossain was the only other Bangladesh batter to reach double figures, contributing 16 runs before falling to Nikhil Chaudhary.
Johnson led the Australian bowling attack with figures of 2 for 6 from his four overs. Adam Zampa claimed 2 for 22, while Ellis took 2 for 21 to contain the hosts throughout the innings.
Mitchell Marsh was adjudged player of the match, while Matt Renshaw player of the series after scoring 113 runs and taking three wickets in three matches, reports UNB.