After a harsh fourth day at the Gabba where Hazlewood suffered a calf injury in the warm-up, India's tailenders helped the visitors avoid the follow-on after going to stumps at 9-252.
With rain washing out close to a full session of play on Tuesday, India looked shot when they slumped to 9-213 and with 33 runs still required to avoid the follow-on in the final session.
But Jasprit Bumrah (10no) and Akash Deep (27no) effectively saved the match for India, putting on 39 for the last wicket before bad light stopped play.
Akash Deep (l) and Jasprit Bumrah helped India avoid the follow-on with a 39-run partnership. (Jono Searle/AAP PHOTOS)
Further downpours are forecast for Wednesday, leaving a draw seemingly inevitable, with both teams likely to leave Brisbane at 1-1.
It means India, as the curent holders, will need to win only one of the last two Tests to retain the Border-Gavaskar Trophy.
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.
After Starc took wickets in his first two overs on Monday, Cummins in particular was brilliant on day four before India's late heroics.
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 Ravindra 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 stand from Bumrah and 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.
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