Spinners Ravindra Jadeja and Kuldeep Yadav left Australia reeling on 236/6.
Australia's batting woes returned on the third day of the fourth Test on Saturday as they hslumped to 236/6 when bad light and rain brought an early end to their response to India's mammoth first innings tally of 622/7 declared.
The tourists only need a draw to claim a first series win in Australia and the home side's hopes of preventing even that faded as they blew a solid start to lose 5 wickets after lunch.
Marcus Harris, Marnus Labuschagne, Shaun Marsh and Travis Head were all dismissed after lunch and Captain Tim Paine followed soon after the tea break.
Peter Handscomb, unbeaten on 28, and fast bowler Pat Cummins, who scored 25, were at the crease when the rainclouds gathered over a Sydney Cricket Ground swathed in pink for the McGrath Foundation breast cancer support charity day.
Most of the Australian batsmen made starts, but only opener Harris was able to get past the half century mark -- his 79 was the highest score by the home side in a series during which India have pillaged five centuries.
Left-hander Harris showed plenty of intent but just when it seemed he could be heading for a maiden Test ton he calamitously played the ball onto his own stumps off Ravindra Jadeja's bowling.
India's disciplined pace attack played a leading role in the victories in Adelaide and Melbourne that gave the tourists a 2-1 series lead coming to Sydney, but it was the spinners who did most of the damage on Saturday.
Jadeja (2/62) also accounted for Shaun Marsh who must surely have exhausted his supply of Test recalls after departing for 8 having left his bat hanging to gift Ajinkya Rahane the simplest of catches at first slip.
Rahane had to work considerably harder for the catch at short midwicket that dismissed Labuschagne (38), diving low to his left to grab the ball with both hands off Mohammed Shami's bowling.
Kuldeep Yadav (3/71) made Travis Head his second victim of the day shortly before tea, the batsman charging down the track to take on the left-arm wrist spinner only to send the ball straight back to him for the catch.
Paine gave the 24 year old his third wicket, a peach of a delivery that clean bowled the Australia captain through his gaping gate for 5.
The surface that India's batsmen had plundered almost at will for two days still offered little movement for the bowlers and the Australians will curse themselves for some soft dismissals after the solid start to the day.
The openers had put on 72 when Usman Khawaja, moved up from number three to replace the dropped Aaron Finch, miscued a slog off Kuldeep to depart for 27 in the opening session.