In between seven rain delays, one aborted start and an early finish due to bad light, Australia were all out for 445 on Monday before Mitchell Starc stamped his authority with the ball.
Further rain is forecast on the final days, meaning the only way Australia may win this game and take 2-1 series lead is if they bowl India out for 245 or less and enforce the follow on in a match for the first time since 2019.
"We've got six wickets to take first," Mitch Marsh said.
"We know we have to take 20 wickets to try and win this Test. All our conversations and planning will be how do we do that.
"Hopefully the weather holds off, and tomorrow is coming in, having a crack, and seeing where we get to."
Led by Starc, Australia's bowlers have at least given them every chance of pulling off a win against an Indian top order becoming more fragile as the tour wears on.
Ground staff have been called upon on numerous occasions on day three at the Gabba. (Jono Searle/AAP PHOTOS)
Starc (2-25) took wickets in each of his first two overs, before a brilliant piece of fielding from the quick gave Josh Hazlewood the chance to remove Virat Kohli.
The left-armer had Yashavi Jaiswal out second ball for four, when the opener inexplicably hit Starc straight to Mitch Marsh at forward square leg.
In Starc's next over he had Shubman Gill caught in the gully, this time wonderfully taken by a diving Marsh moving high to his left.
"Fielding at gully is the most nervous I get, because Cameron Green is probably going to go down as the best ever," Marsh quipped.
"And if you drop one there, they always compare you to Greeny.
"The boys are always into me about how slow I move, or how I can't jump in the field. I probably didn't even need to dive, but I thought it added a bit of mayo."
Mitch Marsh and Mitchell Starc celebrate the spectacular dismissal of Shubman Gill. (Jono Searle/AAP PHOTOS)
It was Starc's fielding that set up Australia's next wicket, when he dived to cut off a KL Rahul hook shot near the boundary and keep it to one run.
Next ball, Hazlewood drew the edge of a driving Kohli to have him caught behind for three, continuing the Indian mega star's horror run in first innings.
A brief seven-ball period on the field between rain delays also allowed Pat Cummins to draw Rishabh Pant's edge and have him caught behind for nine.
Play then resumed for 17 more balls late on, before umpires ended the day with spinners bowling under floodlights.
Rahul has provided India's only resistance, with three immaculate cover drives to the boundary helping him to 33.
Earlier, Alex Carey's 70 helped Australia push towards a large first-innings total, off the back of Steve Smith and Travis Head's day two hundreds.
That is absolutely massive from Alex Carey!— cricket.com.au (@cricketcomau) #AUSvIND pic.twitter.com/G0h3CPKlu0December 16, 2024
Starc (18) also landed some lofty blows off Jadeja and Jasprit Bumrah, before becoming the latter's sixth victim when caught behind.
Bumrah's figures of 6-76 were the best by an Indian at the Gabba. His fellow bowlers collected 4-352 between them.
"We have 11 players, I don't look at it that I have to do extra," Bumrah said.
"We are a new team, a lot of new players have come into the side and we have to look at it that they will learn from the experience."
After rain washed out most of day one, a draw would come as a significant blow to Australia's hopes of regaining the Border-Gavaskar Trophy.
With the series locked at 1-1, India would therefore need to win only one of the last two Tests to ensure at least a drawn series and retain the trophy
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