The Australia captain was 329 not out, the fourth highest score by an Australian and 14th highest by any batsman, when he called an end to the innings just after Mike Hussey reached 150.
India's second innnings got off to a poor start and the tourists lost opener Virender Sehwag for four, reaching tea on 53 for one to add to their first innings of 191.
After tea break India lost Rahul Dravid 29 at 100.
Clarke had brought up the 300 shortly after lunch, flicking the ball through midwicket off the bowling of Ishant Sharma for the 37th four of his majestic innings to become the 21st cricketer to reach the milestone.
The 30-year-old whipped off his helmet to acknowledge a standing ovation from the crowd at the Sydney Cricket Ground and pointed his bat towards his team mates in the home dressing room.
Clarke faced 478 balls and batted for 10 hours and 17 minutes when he waved Hussey off the pitch to another huge ovation from the crowd, keen to leave enough time to bowl India out.
Hussey and his captain had put on 334 for the fifth wicket, eclipsing the previous highest partnership for Australia against India of 288, which Clarke set with Ricky Ponting on Wednesday.
India's batsmen face a Herculean task to rescue the test and keep alive their hopes of winning a first series in Australia but got off to a poor start when Sehwag fell to Ben Hilfenhaus with just 18 runs on the board.
The big paceman swung a delivery across the opener, who slashed it towards David Warner at point and the Australian dived to his left for an athletic two-handed catch.
The embattled Gautam Gambhir, who had raced to 39, and Rahul Dravid, who had made seven, were to resume after the break.
Clarke started the day on 251 and hit a single to mid off on the fourth ball of the morning to edge ahead of England's Wally Hammond for the third highest score in 100 tests at the SCG.
Understandably tired after batting through Wednesday, Clarke took his time to find his batting rhythm but never looked troubled as Hussey kept the scoreboard ticking over at the other end.
A swept four off spinner Ravi Ashwin allowed him to pass Brian Lara's 277 and take second place on the list of top scores at the ground behind Tip Foster, who scored his 278 in 1902-3.
He passed the Englishman's mark to a huge roar from the crowd with a cover drive for four off Sharma 10 minutes before lunch.
Hussey had started the day on 55 and played superbly to reach his 16th test century with a single to third man, a vindication for a player in his mid-thirties with his place in the side under pressure after a poor run of form.
Australia won the first test by 112 runs in Melbourne last week.
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