India have an unassailable 2-1 series' lead after winning the first Test in Adelaide by 31 runs and the third Test in Melbourne by 137 runs.
Australia suffered the indignity of its first follow-on in 150 Tests on a dismal day at the SCG, which was interrupted due to drizzle and bad light.
Selectors will on Wednesday name a squad for the first Test against Sri Lanka, starting in Brisbane on January 24.
Australia won the second test in Perth by 146 runs.
Australia were forced to follow-on on home soil for the first time in 30 years after being dismissed for 300 as India went for the jugular in search of a maiden series triumph Down Under on the fourth day of the final Test on Sunday.
The recalled Peter Handscomb began with objective, confidently stroking two boundaries to move to 37 before swiping at a Bumrah delivery and dragging it onto his stumps.
Kuldeep Yadav, playing his first Test of the series, scalped three wickets, while Ravindra Jadeja took two - this after Australia had made their most assured start of the summer, and were comfortably placed at 128/1. Pacer Mohammed Shami also grabbed a couple of wickets while Jasprit Bumrah managed a wicket as well in the first innings.
The only question is whether Australia will salvage a draw on Monday or the tourists will complete a crushing 3-1 series victory.
Australia were reduced to 236-6 at stumps on day three when bad light had stopped play.
India's Kuldeep Yadav, second left, celebrates with teammates after taking the wicket of Australia's Nathan Lyon.
Tailenders Josh Hazlewood and Mitchell Starc put on 42 for the last wicket before Hazlewood fell for 21 to Yadav.
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.
Kuldeep (5-99) then trapped Nathan Lyon for no score.
Yadav eventually had his man and ended the innings, trapping Hazlewood lbw with a wrong'un.