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Indian opener Yashasvi Jaiswal slammed a majestic 161, but Australia claimed four wickets in the middle session to give themselves a glimmer of hope in the first Test in Perth on Sunday.
At tea on day three, the visitors were 359-5, a lead of 405 runs as they eye victory and a psychological advantage in the five-Test series.
Virat Kohli was not out 40 and Washington Sundar 14.
Jaiswal, who grew up homeless in the slums of Mumbai selling snacks on the streets to survive, was the hero, hitting 15 fours and three sixes in a mature 297-ball stay.
The 22-year-old, in his 15th Test, looked destined for a second career double century, but he clipped Mitchell Marsh to Steve Smith at that point and departed to a standing ovation.
Australia also dropped Devdutt Padikkal (25), Rishabh Pant (1) and Dhruv Jurel (1), after replacing KL Rahul (77) before lunch.
Rahul’s demise ended a record 201-run opening partnership with Jaiswal for India in Australia, eclipsing the previous record set by Sunil Gavaskar and Kris Srikkanth in Sydney in 1986.
The visitors resumed with a 218-run advantage after taking control on day two after Australia were dismissed for a dismal 104 in reply to India’s 150.
Making the score 172-0, Jaiswal hit a risky single off Josh Hazlewood’s opening ball to signal his intention to attack before two boundaries from Mitchell Starc’s first over.
Left-hander Jaiswal, who started on 90, reached triple figures with an extraordinary six off Hazlewood, hitting the boundary head-on, raising his arms triumphantly in the air.
It was his fourth ton and his first in Australia.
Since scoring 171 on debut against the West Indies in 2023, Jaiswal has cemented his place at the top of the rankings.
A telling 214 not playing at home to England this year catapulted him to stardom, but concerns remained about how he would fare in Australian conditions.
After being absent from the first innings, his response against one of the best attacks in the world put all doubts to rest.
As the sun beat down, Australia were finally rewarded for their work when Rahul handed Starc to wicketkeeper Alex Carey.
Playing in place of Rohit Sharma, who stayed home for the birth of his second child, the 32-year-old did a remarkable job supporting his younger partner.
Skipper Rohit is expected to return for the second Test in Adelaide, which will pose a headache for the selectors.
Australia got another breakthrough off the first ball after lunch when Paddikal edged Hazlewood to Smith at slip.
Jaiswal’s dismissal triggered a mini-collapse with three wickets for eight runs before Kohli and Sundar steadied the ship.
Pant charged down the field towards Nathan Lyon and was stumped by Carey while Jurel fell in weight to Pat Cummins.
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