Starc claimed Shadman Islam, caught in the gully by Cameron Green, with the first ball of the second Test in Mackay on Saturday, before ripping through Bangladesh to claim 6-12 and help dismiss the hosts for 64.
He had earlier achieved the feat on three occasions, knocking over Dimuth Karunaratne with the first ball of a Test in Galle in 2016.
He famously cleaned up England opener Rory Burns with the first ball of the Gabba Test during the 2021-22 Ashes and in 2024-25 he dismissed India opener Yashasvi Jaiswal in Adelaide.
With Shadman's dismissal Starc went past the record he previously shared with West Indies quick Pedro Collins, who incredibly knocked over Bangladesh opener Hannan Sarkar with the first ball of a Test three times.
Starc set the tone for the entire 2021-22 Ashes series with his Burns delivery and in Mackay he put Australia on course for victory, despite the hosts being 8-165 at stumps.
The 36-year-old also now has the most first-ball dismissals in either Test innings, with nine, going past England great James Anderson's eight.
"Nothing has changed over 15 years. It is just run in and try and hit the stumps," Starc said after play on day one.
"That has been pretty much it, run in and try and be aggressive and find some swing if it is there to bring the stumps into play.
"It is nice when it comes off and it gets us going in a bowling innings. When you take a wicket first ball it is nice to know you have only got nine more to get."
Starc clearly enjoyed bowling at Great Barrier Reef Arena in Mackay in what is the first Test in the venue's history. He said he had no sympathy for top order batters when they have to contend with a swinging ball in tough conditions.
"Coming from a No.9 batter, I am not going to be handing out batting tips," he said.
"Clearly when the ball does move it creates opportunities. We saw when it was pretty flat last week (in the first Test in Darwin) and the ball was going straight it was pretty easy batting.
"The breeze that comes across the ground here, and the lush square is going to keep the ball quite shiny and we saw it still swinging in the last couple of overs of the day."
Starc also took his career Test wicket tally to 441 for 10th on the all-time list, jumping past South Africa great Dale Steyn (439).
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