In an engrossing end to the fourth day, Jasprit Bumrah and Akash Deep saved India with an unbeaten 39-run last-wicket stand to avoid the follow-on.
India still went to stumps shortly after at 9-252 and a first-innings deficit of 193, but with one more wet day left in a rain-marred Brisbane fixture, the third Test is all but over.
After being joined at the wicket when Ravindra Jadeja was dismissed with 33 still required to avoid being asked to bat again, Bumrah (10no) and Deep (27) essentially saved the game for India.
It means the two teams will likely head to Melbourne at 1-1, with India requiring just one victory from the last two Tests to retain the trophy as current holders.
"The only way to force the game was to enforce the follow-on," Australia's bowling coach Dan Vettori said.
"There was a desperation to get that final wicket and we thought we had a really good chance when Jadeja was dismissed.
"But it was a real fighting partnership from Bumrah and Deep."
Akash Deep (l) and Jasprit Bumrah helped India avoid the follow-on with a 39-run partnership. (Jono Searle/AAP PHOTOS)
Making matters worse for Australia is Hazlewood's injury.
He bowled just one over on Tuesday after being hurt in the warm up, with scans since confirming he had suffered a calf strain and his Test over.
That left Pat Cummins (4-80) and Mitchell Starc (3-83) to get through 44.5 overs between them in India's innings.
"Josh is one of the best bowlers in the world, so it obviously affects the team," Vettori said.
"The weather allowed us to operate with the breaks, it allowed Mitch and Patty to be able to come back on multiple occasions.
"It was a tricky situation at the end where the ball was incredibly soft and getting wet.
"We tried to push them longer to get that last wicket, that was probably the only time we felt they were slightly extended."
After Starc took wickets in his first two overs on Monday, Cummins in particular was brilliant on a fourth day when more than two hours were lost to rain.
Josh Hazlewood bowled just one over on day four before succumbing to a calf injury. (Jono Searle/AAP PHOTOS)
He should have had KL Rahul's wicket on the first ball of the day when the Indian stonewaller edged a ball straight to Steve Smith at second slip, but the veteran spilt the chance.
Rahul went on to add another 51 crucial runs and soak up another 75 balls, before he was eventually superbly caught one-handed by Smith off the bowling of Lyon for 84.
Cummins did have India's out-of-form captain Rohit Sharma caught behind on 10, with a ball that angled in and seamed away.
After Jadeja (77) put on two lengthy stands with Rahul and Nitish Kumar Reddy, it was Cummins who bowled the latter on 16.
And Cummins also had Jadeja well caught by Mitch Marsh, leaving his field back as he tempted the allrounder into a hook shot.
WHAT A CATCH FROM STEVE SMITH!— cricket.com.au (@cricketcomau) Sweet redemption after dropping KL Rahul on the first ball of the day.#AUSvIND | #PlayOfTheDay | @nrmainsurance pic.twitter.com/d7hHxvAsMdDecember 17, 2024
At that point India's chances of avoiding the follow-on looked slim, before the late heroics from No.10 Bumrah and No.11 Akash.
In fading light, Akash hit Cummins over the slips to chalk off the follow-on target, before launching him deep into the stands on what proved to be the last ball of the day.
