After being asked to bat, Bangladesh were bowled out for 131 in 19 overs as none of their top-order batters managed to convert starts into substantial scores.
Saif Hassan provided early impetus with 20 off 14 balls, while returning opener Soumya Sarkar made 17 and stand-in captain Towhid Hridoy struck a quick eight.
Australia's bowlers kept striking at regular intervals. Adam Zampa starred with 3 for 18, while Joel Davies matched him with 3 for 17. Matt Renshaw chipped in with two wickets as Bangladesh slipped from 75 for 4 to eventually lose all ten wickets an over early.
Only Mahedi Hasan offered meaningful resistance in the lower order, finishing unbeaten on 29 off 22 deliveries with four boundaries to lift Bangladesh to a competitive total.
In reply, Australia's chase was anchored by Cooper Connolly, whose aggressive 47 off 27 balls, featuring four fours and three sixes, put the visitors firmly in control. Captain Mitchell Marsh fell for 13 and Josh Inglis managed just five, but Connolly's counterattack swung momentum Australia's way.
After Connolly departed with the score at 78, Bangladesh sensed an opening. Tim David contributed 20 off 16 balls before Mahedi Hasan removed him, while Matt Renshaw struggled to 18 from 28 deliveries. Nikhil Chaudhary's brisk 18 off 13 further eased Australia's path before Bangladesh struck again late in the innings.
The hosts kept fighting through their bowlers. Abdul Gaffar Saqlain, making an immediate impact, picked up 2 for 32, dismissing both Connolly and Renshaw. Mustafizur Rahman, Shoriful Islam, Mahedi Hasan, and Rishad Hossain claimed a wicket each to keep the contest alive.
However, Australia held their nerve in the closing stages. Joel Davies remained unbeaten on seven before Xavier Bartlett sealed the chase with a boundary off the first ball he faced, taking the visitors to 133 for 6 in 18.2 overs.
The victory gives Australia a 1-0 lead in the three-match series, while Bangladesh will look to bounce back and level the contest in the second T20I.
