Starc (5-11) had five wickets by his 22nd delivery as the visitors collapsed in a heap with poor batting to be six down at lunch on day one of the second Test.
Bangladesh had no answer to Starc's swing and pace.
It was the sixth fastest five-wicket haul in Test history, seven balls shy of Starc's own all-time record of 15 deliveries against the West Indies in Kingston last year.
The left-arm quick took his tally of Test wickets to 440 and 10th on the all-time list, going one past South Africa great Dale Steyn.
Pat Cummins won the toss and inserted the visitors, with Starc's pace and swing proving too hot to handle.
Opener Shadman Islam played across a swinging delivery and edged straight to Cameron Green in the gully, just as the sold-out crowd at Great Barrier Reef Arena settled into their seats.
Shadman was the first of three left-handers to disappear into the pavilion for ducks inside Starc's opening eight deliveries.
A lazy waft by Tanzid Hasan presented third slip Beau Webster with a gift and next ball captain Najmul Hossain Shanto was trapped in front.
The umpires checked to make sure Tanzid's shot wasn't a bump ball, as they did off the last ball of Starc's third over when Mominul Haque (nine) edged to Green with a woeful prod to a wide half-volley.
The outcome was the same and Starc had an incredible 4-4 off three overs.
Webster, much to the dismay of Starc, dropped an absolute sitter in the slips off Litton Das but it made no difference.
The next ball Starc had his fifth wicket when he successfully reviewed an lbw shout, to the relief of Webster.
Cummins was the only other wicket taker for Australia.
Alex Carey and Cummins had spoken before the Test about their determination to atone for the nine-wicket loss to Bangladesh in Darwin.
From the first ball Starc was switched on and the slips, apart from one glitch, took their catches.
Australia announced on match eve Queensland left-hander Matt Renshaw would open the batting after Jake Weatherald was axed.
Bangladesh made just one change to the side that won by nine wickets in Darwin with left-arm quick Shoriful Islam replacing Ebadot Hossain.
Shoriful has recovered from a side strain that kept him out of the first Test.
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