And a superb 150 by Michael Hussey left Australia poised for a big win.
Clarke made the highest individual Test score at the SCG and the fourth-best tally by an Australian batsman in Test history - before declaring his team's first innings closed at 4-659.
The Indians, set a mammoth 468 runs to chase, were met by a fired-up Ben Hilfenhaus who ended the day's play with 2-37, after dismissing Virender Sehwag (4) and Rahul Dravid (29).
At stumps India were 2-114, still needing a further 354 runs just to make Australia bat again with Gautam Gambhir not out on 68 and Sachin Tendulkar unbeaten on eight.
Clarke and Hussey combined in an unbroken 334-run partnership to help post Australia's largest team total since July 2009, when they made 6(dec)-674 against England in Cardiff.
It was also the first time since that Ashes Test that three or more batsmen have scored centuries for Australia, with Ricky Ponting posting 134 on day two.
It completed a remarkable turnaround for the hosts who lost just one wicket for 622 runs after Clarke joined Ponting at the crease when Australia were 3-37 on day one in pursuit of India's 191.
In the 100th Test match played at the historic SCG, Clarke obliterated the previous highest individual score at the ground of 287 set by Reginald Foster back in 1903 - and the first triple hundred in Sydney was greeted with a huge roar by the crowd.
In the end, Clarke batted for 617 minutes, hammering 39 fours and one six.
On day two, Clarke and Ponting set the mark for the highest partnership against India with 288, but it lasted less than a day - as Hussey came out to bat with the skipper and amass the fourth-largest partnership seen at the SCG.
India's bowlers were humiliated, with all of their front-liners going for well over 100 runs each with Zaheer Khan (3-122) the pick of the bunch thanks to his three wickets on day one.
Australia's momentum continued after the declaration with David Warner snaring a sharp catch off the bowling of Ben Hilfenhaus (2-37) to remove dangerous opener Virender Sehwag for four.
But an 82-run stand between Gambhir and Rahul Dravid (29) gave India some momentum before Hilfenhaus bowled Dravid to bring Tendulkar to the crease.
Gambhir survived a late chance when he was dropped by Brad Haddin and India will be hoping he and Tendulkar can carry on if the tourists are going to push the game into a fifth day.
- With AAP