The Australians took an unbeatable 2-0 lead in the three-match series when they cruised to 118 for two, led by an impressive Shaun Marsh half-century, in reply to Bangladesh's meagre tally of 117 after winning the toss.
This lopsided result came after Bangladesh were dismissed for a record low 74 in a 180-run defeat on Sunday.
In Darwin, the tourists were again in trouble from the moment they arrived at the crease and lasted just 36.1 overs.
Bangladesh's decision to bat first backfired immediately when the first ball of the innings saw Tamim Iqbal caught by David Hussey from the bowling of Nathan Bracken for a golden duck, after the left-hander got an outside edge to a ball that swung away late.
It set the tone for the rest of the innings, as a ruthless Australia quickly capitalised on some good early movement with the ball.
Bangladesh captain Mohammad Ashraful carried his team's hopes but made just three before getting a thick outside edge when he attempted to drive Stuart Clark, Cameron White taking a sharp catch at first slip as the visitors slumped to 15 for three in a disastrous start.
Junaid Siddique (21), back in the team due to a finger injury to Raqibal Hasan, and Shakib Al Hasan (19) finally offered some resistance, putting on 38 for the fourth wicket, but once their partnership was broken Bangladesh slumped again to 59 for six.
Dhiman Ghosh briefly lifted Bangladesh spirits when he lofted the leg-spin of White over mid-wicket for a six and four in successive balls to bring up their century, but when he went for 30, off 36 balls, his side crumbled again and the last three wickets fell for just 13 runs.
Five of the six Australian bowlers used tasting success, Mitchell Johnson leading the way with 3-17.
The home side was barely troubled in reply and needed just 22.4 overs to reach the target, although Bangladesh spinner Shakib Al Hasan (2-38) impressed by picking up both wickets to fall.
He trapped Shane Watson lbw for 29 before having Australian captain Michael Clarke stumped for one after an impetuous shot.
Marsh continued his emergence as an international batsman and rarely looked troubled in making an unbeaten 69.