Mitchell Starc looked to be back to his best as he took the Bangladesh lower-order to the cleaners, taking four wickets as the Asian side went from 181-6 to 182 all out.
Australia earned a single point from the first match of their campaign against New Zealand which had to be abandoned due to rain. This has happened after rain washed out their first match against New Zealand.
"Their batsmanship is ridiculously unbelievable, they know the game inside out and it's a master class when they get going".
While Bangladesh slumped to an eight-wicket defeat against hosts England in the tournament opener, Australia's first match against New Zealand was largely affected by rain before it was eventually abandoned, and both the Trans-Tasman rivals earned a point each.
Steve Smith's side were on course for a comfortable victory after bowling out the Tigers for 182, then cruising to 1/83 after 16 overs, before the rain began to fall in south London.
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Here, they had the upper hand as they calmly moved towards Bangladesh's total.
Australia captain Steve Smith: "It's a little bit frustrating not to get a result in".
Beaten by England last week, Bangladesh must win to keep their last four hopes alive.
Australia's bowlers found the rhythm that had been missing against New Zealand, and Tamim - who made a century against England on Thursday - seemed to be the only player able to navigate the bowlers.
Hasan scored 29 runs, hitting just two boundaries in the 48 balls he faced.
The Australian paceman bowled Mashrafe Mortaza two balls later, took out the stumps of Rubel Hoosain with his next delivery and came within inches of a hat trick as another swinging yorker flashed past Mustafizur Rahman.
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"In today's match Australia was far ahead of us, but in the last match against New Zealand, Australia were in the same position [as us] so you can't do anything with the weather", Mortaza said.
Legspinner Adam Zampa, preferred to John Hastings by the selectors, picked up two wickets with Travis Head, Hazlewood, Pat Cummins and Moises Henriques grabbing one apiece.
Starc ripped through the Bangladesh tail with a venomous display of fast bowling, to finish with 4-29.
Otherwise, if they lose tonight, they have to beat Bangladesh on Friday (NZT) and then hope England can beat Australia.
"Australia were unlucky and we are lucky to still be in the tournament".
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