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.
It's also the first time in 142 years of Test cricket history that a visiting side have had the option of asking Australia to follow on twice in a home summer.
India leads the four-Test series 2-1 after wins in the first test at Adelaide by 31 runs and last week's Boxing Day Test in Melbourne to retain the Border-Gavaskar trophy.
India have all but confirmed their first series Test victory in Australia by batting for almost two full days in raising 622-7 declared with Pujara (193) and Pant (159 not out) scoring centuries.
Sunday's 322-run deficit is also the third-largest in Australia's history at the SCG, and their biggest since 1936.
The only question is whether Australia will salvage a draw on Monday or the tourists will complete a crushing 3-1 series victory.
Kuldeep Yadav registered his second five-wicket haul in Test cricket.
Josh Hazlewood was dropped by Hanuma Vihari off Kuldeep's bowling when he had yet to score and he and fellow tailender Mitchell Starc (29 not out) fought a dogged rearguard to put on 42 for the final wicket.
Australia, who had not been asked to follow on at home since 1988, reached 6-0 in their second innings when bad light resulted in play being abandoned for the day. Kuldeep then picked Nathan Lyon leg-before with a full toss that hit the boot but Lyon didn't review, even when the impact looked dicey, much to the frustration of Ricky Ponting on air, who called Australia "slack and not desperate enough".
Bumrah needed just four balls at Peter Handscomb to remove the recalled batsman for 37, tempting him to play a delivery outside off that took the inside edge and dislodged the bails.
Yadav eventually had his man and ended the innings, trapping Hazlewood lbw with a wrong'un.