India were battling to avoid defeat against Australia after losing two wickets before the close of play on Sunday in a third Test marred by allegations of racist abuse from the Sydney crowd.
The hosts declared their second innings at tea on day four at 312 for six, leaving India needing a mammoth 407 to win and they reached 98-2 at stumps, still needing a further 309 runs with the four-match series locked at 1-1.
No team has ever bettered 288 to clinch victory in the fourth innings at the Sydney Cricket Ground, with Australia achieving that mark against South Africa in 2006.
India's record run chase started steadily before losing openers Shubman Gill for 31 and Rohit Sharma for 52, leaving their hopes resting on Cheteshwar Pujara, who was nine not out, and captain Ajinkya Rahane, unbeaten on four.
Sharma and Gill lived dangerously against some early torrid bowling by Josh Hazlewood and Pat Cummins.
But they settled in and began playing their shots, with the graceful Sharma bringing up an 11th Test 50 before being caught at fine leg hooking a Cummins short ball.
Gill, who has cemented his place in the side after making a debut this series, again looked at home until he nicked a Hazlewood delivery to Tim Paine behind the stumps on 31.
Australia's declaration came after Green fell on the stroke of tea for an entertaining 84, his maiden Test half-century, with captain Tim Paine unbeaten on 39.
Steve Smith made 81 and Marnus Labuschagne 73, with Ravi Ashwin and Navdeep Saini grabbing two wickets each.
Just before the break there was a near 10-minute interruption to play that saw six fans removed after Mohammed Siraj, fielding on the boundary, complained to the umpire.
It was not clear what was said, but the incident followed India lodging a complaint on Saturday after allegations of racist abuse towards the team by sections of the crowd.
The International Cricket Council launched an investigation with Cricket Australia apologising to India and vowing anyone at fault faced "lengthy bans, further sanctions and referral to NSW Police".
- Green sixes -
Australia had resumed the day on 103 for two after India were bowled out for 244 in the first innings in reply to Australia's 338, with Smith on 29 and Labuschagne 47.
Labuschagne should have fallen second ball, but an appalling error by Hanuma Vihari left bowler Jasprit Bumrah clutching his face in disbelief.
Labuschagne flicked a delivery at knee height for what should have been a regulation catch, but it somehow hit Vihari's wrist and went to ground.
It was another setback for a side without the spin of allrounder Ravindra Jadeja after he was hit on the left thumb batting on Saturday.
He didn't take the field with Indian media saying it was dislocated and he would only bat again "if required", with the injury likely to rule him out of the fourth Test next week.
Rishabh Pant also took a blow to his elbow while batting and was another no-show with Wriddhiman Saha keeping wicket.
However, his injury was not believed to be as bad as Jadeja and he was expected to bat in the run chase.
Labuschagne brought up back-to-back 50s and looked comfortable until Saini snapped his 103-run partnership with Smith.
Matthew Wade quickly went for four, and it proved slow going for Smith.
But following his first innings 131, he kept his focus to notch another half-century, ably accompanied by Green, until trapped lbw by his nemesis Ashwin.
Green, 21, again showed composure to help solidify his place in the team, bringing up his 50 with a boundary then smacking three huge sixes before caught by Saha off Bumrah as he swung the bat again.
Migrants in a dinghy crossing the English Channel
Sunder Katwala