Sachin Tendulkar's unbeaten 154 put Australia's 15-match winning streak under threat.
The little master guided India to a first-innings lead of 69 on day three of the second Test.
In reply to Australia's 463, India were bowled out for 532 and the home side reached 0-13 in five overs before stumps at the SCG.
The day belonged to Tendulkar, who has scored 652 runs at the amazing average of 326 in four Tests at the ground.
"Yes I can say that this is one of my favourite grounds. I really enjoy batting here every moment," said Tendulkar, who hit 14 fours and one six from 243 balls.
"It has truly been a memorable one here. All my outings have been good.
"Sometimes you walk on the field and it gives you a good feeling. It's one of those grounds where I really enjoy batting.
"When you perform well against the top side, it's wonderful.
"Right now it's nicely poised, it's evenly poised. We will have to put up a good show (Saturday) and win more sessions."
Australia's leading paceman Brett Lee took 5-119 in a courageous performance on a bat-friendly pitch, his eighth five-wicket haul and first at his home ground.
Tendulkar's 160-ball hundred drew prolonged applause from the 29,358 spectators who soaked up the moment in what could be the 34-year-old strokeplayer's final tour of Australia.
"Australians are known for that. They enjoy competitive cricket," Tendulkar said of the SCG crowd, which included thousands of Indian fans.
"They understand the game very well so it's truly a pleasure to be out here in the middle and score some runs in front of the Australian crowd."
Australia had been attacking hard after lunch through Lee, who was causing headaches with the second new ball as India lost 4-52 to be 7-345.
But Test cricket's second-leading runscorer found a reliable partner in the aggressive Harbhajan Singh, who made 63 in a partnership of 129, a record for India for the eighth wicket against Australia.
"He was definitely in the tail's ear saying to try and get their heads down," Lee said of Tendulkar.
"And I know when Harbhajan came in he started playing a few shots and Sachin went up and had a few words to him and Harbhajan batted like a No.3 batsman.
"He's great with the tail. The way that he batted, he played all the shots and was nice and patient and that's the reason why he's got 38 Test hundreds."
Resuming on 3-216 following VVS Laxman's 109, India lost Sourav Ganguly for 67 and Yuvraj Singh for 12 in the morning session.
Ganguly was out in limp fashion as he gave a catch to mid-off from the bowling of spinner Brad Hogg (2-121).
The former Test skipper showed his displeasure by childishly smashing his bat into the pitch.
Yuvraj, who failed twice (0 and 5) in last week's Melbourne Test defeat, was lbw to Lee in the third over with the second new ball.
Lee struck again shortly after lunch, removing Mahendra Singh Dhoni (2) and Anil Kumble (2) in consecutive overs, both caught behind as Adam Gilchrist became the second wicketkeeper in Test history to claim 400 dismissals behind South Africa's Mark Boucher (408).
All-rounder Andrew Symonds, who appeared to suffer an ankle injury while fielding, did not bowl but stayed on the field. Lee said the Queenslander had indicated he was fine.
Symonds made a career-best 162 not out in Australia's first innings.
Australia lead the four-match series 1-0 and victory in Sydney would give Ricky Ponting's side a world record-equalling 16 consecutive wins.