The hosts went to lunch at 3-71 chasing 162 for a Test and series win after Scott Boland (6-45) completed a six-wicket haul to help skittle India for 157 within 45 minutes of Sunday's restart.
In reply, openers Sam Konstas (22) and Usman Khawaja put on 39 runs in the first 23 balls before quick Prasidh Krishna (3-27) spearheaded a fightback that put the tourists back in the game.
Prasidh Krishna has spearheaded India's pace attack in Jasprit Bumrah's absence. (Dan Himbrechts/AAP PHOTOS)
Steve Smith (4) notably clipped to Yashasvi Jaiswal as the third of Prasidh's scalps, stranded one run shy of becoming the fourth Australian to make 10,000 in his Test career.
He will need to wait until the upcoming Test tour of Sri Lanka to join Ricky Ponting, Allan Border and Steve Waugh in the illustrious club of 14 Test batters.
Steve Smith departed one run shy of 10,000 runs for his Test career. (Dan Himbrechts/AAP PHOTOS)
With talisman Jasprit Bumrah off the pitch nursing a bad back, Indian opening bowlers Mohammad Siraj and Prasidh went for 26 runs in the first two overs to open the door for the hosts.
Openers Konstas and Khawaja signalled their positive intent from the outset on a fiendish SCG wicket, the 19-year-old opener notably slapping Siraj past cover for four in the first over.
Having dropped captain Rohit Sharma at the SCG, India cried out for the composure of stand-in skipper Bumrah, showing their nerves in the absence of the series' most influential man.
An Abhimanyu Easwaran misfield leaked four runs on the boundary in the most egregious example of India's ill discipline, with the visitors giving up 15 runs from sundries.
But they'd have felt renewed confidence when showman Konstas mindlessly slogged a catch high to Washington Sundar at mid off after slamming three boundaries in his 17-ball cameo.
Sam Konstas played freely before offering up a catch. (Dan Himbrechts/AAP PHOTOS)
Prasidh had Marnus Labuschagne (6) caught behind and Smith fell the same way shortly after.
Khawaja (19) and Travis Head (5) are unbeaten at the crease.
Earlier, Boland (6-45) confirmed the second five-fer of his Test career when Siraj edged him to Khawaja in the slips for the ninth wicket around 40 minutes after the restart.
Boland has made use of an atypically green SCG wicket, finding plenty of movement en route to 10 wickets for the game - and a headache for selectors ahead of the upcoming Sri Lanka tour.
The softly-spoken Victorian has never taken as many in a match during 13 years of first-class cricket.
Bumrah returned to the pitch after leaving the SCG to go for scans and sending a scare through the Indian camp on day two.
But he had little chance to showcase his movement or lack thereof; India's innings was over when Boland bowled him on only the third delivery he faced.
India were into the bowlers only 10 minutes after play began on Jane McGrath Day, the pink crowd in raptures when Ravindra Jadeja clipped Pat Cummins to Alex Carey behind the stumps.
The pink Test crowd had plenty of action to cheer on day three at the SCG. (Dan Himbrechts/AAP PHOTOS)
Captain Cummins (3-44) then collected Sundar's middle stump to signal the end was nigh for the tourists.
Should Australia lose in Sydney, India will draw the series 2-2 and retain the Border-Gavaskar Trophy, having won the last four Test series between the two cricketing powerhouses.
A defeat would also leave Australia relying on results during their upcoming tour of Sri Lanka to confirm a spot in the World Test Championship Final over winter.
