India will resume 98/2 on the final day of the third test against Australia, still, 308 runs behind the hosts with a full day of batting ahead of them.
Openers Shubman Gill (31) and Rohit Sharma (52) were winkled out by the Australian pace attack in the final session, leaving Cheteshwar Pujara, who (9no), and skipper Ajinkya Rahane (4), to continue the fight.
With no rain forecast for Monday, the tourists face a tough day batting on a deteriorating wicket if they are to avoid going 2-1 down in the series, before they head to Brisbane for the final test.
The engrossing contest was marred for the second successive day by complaints from the Indian team that they were being racially abused by a section of fans in the crowd, that was limited to 7,225 by COVID-19 restrictions.
Bowler Mohammed Siraj approached the umpire and the match was paused while a small group of fans were removed from the ground by police. Cricket Australia apologised to the India team and promised a full investigation of the incidents.
Australia declared at tea on 312/6 on the back of a maiden test half-century from all-rounder Cameron Green (84) along with useful contributions from Marnus Labuschagne (73) and Steve Smith (81).
That left India needing 407 runs to win the match, a highly improbable target given the highest successful fourth-innings run chase at Sydney Cricket Ground was the 288/2 Australia scored to beat South Africa in 2005-6.
India were missing Ravindra Jadeja's left-arm spin bowling and Rishabh Pant behind the stumps, after they sustained a dislocated thumb and an elbow injury respectively on Saturday.
Paceman Jasprit Bumrah was again the pick of the Indian bowlers and would have dismissed Labuschagne off the second delivery of the day had Hanuma Vihari held onto the catch at square leg.
Sharma later helped Tim Paine avoid a duck when he dropped a catch off Bumrah in the slips, the Australia skipper going on to make 39 not out.
The rest of Australian runs came from the usual suspects with Labuschagne making the most of his reprieve to notch up his 10th half-century in 17 tests.
Smith, who scored 131 in the first innings, looked to be heading for another century when Ashwin referred an lbw decision to DRS and the batsman was sent on his way for 81, the third time in the series he has fallen to the spinner.
Green was cautious, before reaching the half-century mark, but then accelerated with the declaration insight, plundering four big sixes before getting a faint edge to a Bumrah delivery.
Australia coach Justin Langer, who joined in the condemnation of the alleged racial abuse, said his side still faced a tough challenge to wrap up the victory.
"There's very little in this wicket," he said. "We're going to have to squeeze really hard, keep the pressure up. Hopefully, there's a little bit of spin tomorrow for Nathan Lyon and we'll just keep doing what we're doing."