Ponting piled on 140 following Matthew Hayden's 103 on day three, while Michael Clarke, middle order batsman, also scored a ton with an impressive 118.
However wicketkeeper-batsman Adam Gilchrist, who announced his retirement from cricket on Saturday, fell cheaply for 14 in what is likely to be his last Test innings.
At stumps India were 45 for 1 in their second innings, with Virender Sehwag on 31 and Rahul Dravid on 11, after makeshift opener Irfan Pathan was dismissed for a duck, LBW to Mitchell Johnson.
Clarke, who dropped Sehwag when the Indian opener was on two, said Australia would need all their quality to grab an unlikely victory.
"It's going to be hard, I think we're going to have to bowl really well," Clarke said.
|"When he came out to bat we clapped for him to show that respect. He has actually changed Test cricket."|
Indian all-rounder Irfan Pathan
on Adam Gilchrist
"Once the ball gets a bit soft it'll be hard for India to score and we'll get a bit of reverse swing with the quick bowlers and Brad Hogg, Andrew Symonds and hopefully myself can play a big part tomorrow as well because there's just enough there for the spinners."
Pathan, who took 3 for 112 off 36 overs, said India still believed they could level the series, which Australia lead 2-1.
"We have to bat well tomorrow and if we put some runs on the board, Australia has to bat last and so many matches have changed on the last day," the all-rounder said.
Ovation for Gilchrist
Gilchrist, who holds the Test wicketkeeping record for most dismissals, received an enormous ovation as he strode on to the Adelaide Oval, with the crowd chanting 'Gilly' and the Indians lining up to applaud him.
"He has been a wonderful cricketer and we all respect him," Pathan said.
"When he came out to bat we clapped for him to show that respect. He has actually changed Test cricket."
Gilchrist got off the mark from the fifth ball, with a crisp straight drive off Ishant Sharma.
The 36-year-old almost took out umpire Billy Bowden with a typically thundering straight drive for four off Pathan, but a moment later the bowler had his revenge when Gilchrist slashed a wide delivery straight to Sehwag at cover.
Gilchrist made just 14 from 18 balls in an all-too-brief glimpse of his batting genius, and again got a rousing ovation from the crowd and his opponents as he trudged off, with Sharma running up from fine leg to shake his hand before he left.
Earlier, Ponting bounced back to form with his 140, equalling Gavaskar and West Indian Brian Lara's mark of Test centuries, but still has a way to go to catch Sachin Tendulkar, who has 39 centuries.
Ponting, who went into the match with a series average of just 20.33, batted with a runner towards the end of his innings because of a sore back and did not take to the field in India's second innings.