England will resume at 6-134 on day four of the second Test at the Gabba, still 43 runs behind Australia after surprise top-scorer Starc compiled 77 to help the hosts to 511 in their first dig.
England's reply started impressively but Starc (2-48) took the huge wicket of first-innings centurion Joe Root (15) as Australia stymied their sloppy visitors.
"He's a special player," said Starc's fellow paceman Michael Neser.
"He doesn't like to admit it, but he is the GOAT. The greatest leftie of all time.Â
"He does it with the ball, the bat, and to be next to him, witnessing what he does, is just amazing."
Batting collapses have been a theme for the tourists this series and they lost 6-80 as Australia hit superb lengths under lights after dinner.
England's extremely remote hopes of levelling the series in Brisbane now hinge on allrounders Ben Stokes (4no) and Will Jacks (4no).
"Tough day, obviously we're not in a great position," said England assistant coach Marcus Trescothick.
"Australia getting ahead of the game and putting us under pressure, of course, that's never great, sitting there watching that."
Stokes' men will be left to defy history if they lose; no England side has recovered from 2-0 down to win a five-match Ashes series.
Neser (2-27) went some way to justifying his controversial selection at the expense of Nathan Lyon with two caught-and-bowled efforts after dinner.
Having dropped opener Ben Duckett for six, Neser stretched up to send Ollie Pope (26) packing and then took a low catch from Zak Crawley (44), who again made a start after a good first dig.
Scott Boland (2-33) broke an impressive 48-run opening stand that had England off to a flyer and then had Harry Brook (15) caught behind.
Boland bowled Duckett (15) to continue an unhappy match for the opener, who managed a golden duck in the first innings and dropped two catches in the field.
But Starc had the biggest wicket of all, preventing Root from reprising the unbeaten 138 from the first innings that had put England well in the contest.
Australia rejoiced as their review picked up an outside edge from the former captain, with Jamie Smith (4) then also edging Starc to Alex Carey.
With the bat earlier, Starc had to navigate the second new ball as well as the loss of dangerous batting partner Carey (63) en route to his highest Test score since 2016.
When Carey nicked off, Australia's innings appeared likely to peter out as they held a solid, though certainly not watertight, 82-run lead.
But by the time No.9 Starc holed out to Ben Stokes at mid-off, Australia had beefed that advantage up 75 more runs.
They'd also slowed the pace of the game down to ensure England would need to face the day-night masters bowling with a new pink ball in fading light.
"It actually went perfectly, the way 'Starcy' went about it," Neser said.
"It put us in a great position to be bowling under lights with that new pink ball."
Starc had raised his bat for a 12th Test half-century just after tea and then put his foot on the accelerator with back-to-back fours off Gus Atkinson (1-114).
No man in Test history has scored more runs at No.9 than Starc, who passed former Ashes rival Stuart Broad during Saturday's second session.
Earlier in the game, he had taken six wickets and dethroned Pakistan's Wasim Akram as the most prolific left-arm pace-bowler in Test history.
Just when his Test best of 99 appeared in danger, Starc sent a short Brydon Carse (4-152) delivery to Stokes and left the pitch to a standing ovation.
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