India still need another 30 runs to guarantee Australia start their second innings after going to lunch on day three at 7-244.
After resuming on Saturday at 5-164, free-wheeling Pant (28) and star allrounder Ravindra Jadeja (17) were dismissed during the first session.
Allrounders Nitish Kumar Reddy (40no) and Washington Sundar (5no) are the last recognised batters, with star quick Jasprit Bumrah and fellow pacer Mohammed Siraj at the end of the long Indian tail.
Pant, the hero of India's famous series win in Australia four years ago, departed in reckless fashion when he mis-hit a Scott Boland (3-37) delivery to Nathan Lyon at third man.
The previous delivery, Pant had been hit in the midriff by Boland while attempting almost the same shot.
Pant also fell over in the process of attempting to play the leg-side shot that was his downfall, prompting Gavaskar to call it a "shocking" way to depart.
— Express Sports (@IExpressSports) #RishabhPant #AUSvIND Sunil Gavaskar after Rishabh Pant's dismissal on ABC: "He should not be going in that [India's] dressing room, he should be going in the other dressing room."https://t.co/kUpZyKG75wDecember 28, 2024
"Stupid, stupid, stupid," an exasperated Gavaskar said on ABC Radio.
"You missed the previous shot, and look where you've been caught. That is throwing away your wicket.
"You cannot say that that's your natural game. That is letting your team down badly.
"You have to understand the situation as well.
"He should not be going in that (India's) dressing room, he should be going in the other dressing room."
Australia remain in the box seat to grab a 2-1 lead in the Border-Gavaskar series.
India will retain the Border-Gavaskar trophy if they pull off an extraordinary comeback victory in Melbourne.
Australia need to prevent the tourists from winning one of the last two Tests in this series, while claiming at least one themselves to regain the trophy for the first time since 2014-15.
Cruising at 2-153 just 30 minutes before stumps on day two, India lost 3-7 following a calamitous mix-up between Virat Kohli and Yashasvi Jaiswal.
Star veteran Steve Smith top-scored with 140 in Australia's 474, but his innings was overshadowed by the debut brilliance of teenager Sam Konstas.