Openers Usman Khawaja (4) and Marcus Harris (2) safely negotiated four overs until bad light and light drizzle forced an early end to an already heavily rain-disrupted day just before the re-scheduled tea break.
Australia will resume on six without loss on Monday, still without a century in the series and 316 runs adrift of India's mammoth first innings effort of 622-7 declared.
The tourists, leading 2-1 in the four-test series, only need a draw to secure a breakthrough triumph in Australia but skipper Virat Kohli did not hesitate to send the hosts back in when they fell well short of the 423 runs needed to avoid the follow-on.
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"Yesterday, when they were about 150 for five, we looked at the weather forecast and decided would definitely enforce the follow-on if we could get them out," India bowling coach Bharat Arun told reporters.
"It's a great opportunity for us to make it 3-1 and that's a big motivation for us."
Play at the Sydney Cricket Ground finally got underway after a rain delay of almost four hours with the hosts resuming on 236-6, and India needed just 80 minutes to take the remaining Australian wickets at a cost of 64 runs.
Mohammed Shami set India on their way when he took the second new ball immediately and removed Pat Cummins's off stump with the sixth delivery of the day to dismiss his fellow paceman for 25.
KULDEEP CLAIMS FIVE
Peter Handscomb, recalled for his ability to play spin, followed for 37 after adding nine runs to his overnight tally, dragging the ball onto his stumps to give quick Jasprit Bumrah his first wicket of the match.
Nathan Lyon faced just five balls before he was adjudged lbw to fellow spinner Kuldeep Yadav for a duck, a decision Australia opted against reviewing despite a question mark over whether the ball would have hit the stumps.
Josh Hazlewood was dropped by Hanuma Vihari off Kuldeep's bowling when he had yet to score and he and fellow tail-ender Mitchell Starc (29 not out) fought a dogged rearguard to put on 42 for the final wicket.
Left-arm wrist spinner Kuldeep (5-99) finally got his man to secure a second five-wicket haul in his sixth test, though, trapping Hazlewood leg before wicket for 21, in a decision confirmed after a review.
England were the last team to force Australia to follow-on at home in the drawn 1988 Sydney test, a result the hosts are unlikely to repeat unless the weather intervenes decisively.
"It hurts mate, you never want to follow-on in any cricket match," Handscomb said.
"Huge for us to push for the draw tomorrow, we've obviously got a really good chance to shift some momentum back into our camp -- not just for the one-dayers coming up but for the World Cup and the Ashes (against England).
"This movement can really start tomorrow... if we can last this day and show the country, show the world, that we're not far from being a really good team."
(Reporting by Nick Mulvenney; Editing by John O'Brien/Peter Rutherford)
