The tourists, who declared on 622-7 late on Friday, only need a draw to claim a first series win Down Under and Australia’s hopes of salvaging anything from the match faded with the loss of five wickets after lunch.
Marcus Harris, Marnus Labuschagne, Shaun Marsh and Travis Head were all dismissed in the second session, before captain Tim Paine followed shortly after the tea break.
Peter Handscomb, unbeaten on 28, and fast bowler Pat Cummins, who had made 25, were at the crease when bad light stopped play at a Sydney Cricket Ground swathed in pink for the McGrath Foundation breast cancer support charity day.
A storm lashed the venue for the final hour of scheduled play and proceedings will resume 30 minutes early at 10 a.m. local time on Sunday.
Most of the Australian batsmen made starts but only opener Harris was able to get past the half-century mark, his 79 the highest score by the home side in a four-match series in which India have pillaged five centuries.
The left-hander showed plenty of intent but just when it seemed he could be heading for a maiden test ton, he played the ball onto his own stumps off the bowling of Ravindra Jadeja.
Jadeja also accounted for the experienced Marsh, who must surely have exhausted his supply of test recalls after leaving his bat hanging to gift Ajinkya Rahane the simplest of catches at first slip.
Rahane had to work considerably harder for the catch that dismissed Labuschagne for 38 off the bowling of Mohammed Shami, diving low to his left to grab the ball with both hands.
Australian skipper Tim Paine became Kuldeep Yadav’s third victim when a peach of a delivery clean bowled the Australia captain through his gaping gate for five.
The 24-year-old’s best delivery, though, was probably the wrongun that deceived Usman Khawaja into miscuing a slog in the first session and sent Australia’s top batsman packing for 27.