India, despite a fine spell from paceman Ben Hilfenhaus, were 114-2 at the close of play with opener Gautam Gambhir (68) and Sachin Tendulkar, who had made eight from 42 balls, set to resume on day four.
The Australia captain's triple century was just the 25th in Test cricket, the fourth highest test score by an Australian, 14th highest by any batsman and highest in 100 tests over more than a century at the SCG.
More importantly for Australia, with support from Ricky Ponting (134) and Mike Hussey (150 not out), Clarke's innings rescued the hosts from 37-3 and put them in an excellent position to take a 2-0 lead in the four-match series.
Clarke brought up the 300 shortly after lunch, flicking the ball through midwicket off the bowling of Ishant Sharma for the 37th four of his innings, becoming the 21st cricketer to reach the milestone.
The 30-year-old right-hander whipped off his helmet to acknowledge a standing ovation from the 31,000 crowd at his home ground and pointed his bat toward his teammates in the dressing room.
Selflessly passing up the chance to break any more records, Clarke called time on his best test innings a ball after Hussey had reached his 150 to leave his bowlers two-and-a-half days to bowl the tourists out.
Clarke had faced 478 balls, batted for 10 hours and 17 minutes and scored 40 boundaries when he left the pitch to another huge ovation from a crowd largely dressed in pink in honor of former paceman's Glenn McGrath's breast cancer charity.
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.
Australia's pace attack, which dismissed India for 191 in their first innings, made an early breakthrough when Hilfenhaus removed opener Virender Sehwag for four courtesy of an athletic catch from David Warner with just 18 runs on the board.
The big paceman returned to bowl Rahul Dravid through the gate for 29 with a beautiful delivery and he and James Pattinson ensured Gambhir and Tendulkar had anything but a comfortable passage to stumps.
Clarke started the day on 251 and, understandably tired after batting through Wednesday, took time to find his rhythm even if he never looked troubled as Hussey kept the scoreboard ticking over at the other end.
A cover drive for four off Ishant Sharma 10 minutes before lunch allowed him to pass Englishman RE Foster's high score of 287 at the SCG but he was forced to wait until after the break to reach the 300.
Hussey had started the day on 55 and played superbly to reach his 16th test century, vindication for a player in his mid-thirties with his place in the side under pressure after a poor run of form.
India's batsmen face a Herculean task to rescue the test and keep alive their hopes of winning a first series in Australia. They lost the opener in Melbourne by 122 runs last week.
