Australia's elder statesmen put on a partnership of 79 to take Australia to 3-116 at the end of the first day, after India had earlier been demolished for 191 and the hosts then crumbled to 3-37.
With Ponting unbeaten on 44 and Clarke not out on 47, the late resurgence was in stark contrast to the rest of the day, which saw wickets fall with alarming regularity.
James Pattinson had torn through India's top order earlier, removing big guns Sachin Tendulkar, Virender Sehwag, VVS Laxman and opener Gautam Gambhir for figures of 4-43.
Peter Siddle (3-55) bowled superbly to move to 100 Test scalps, and Ben Hilfenhaus (3-51) moved the ball nicely and was also rewarded by cleaning up the tail as India were all out for 191 after tea.
They're in untouchable form at the moment, but the pace trio would have struggled to get a look in against New Zealand and India if not for injury.
Pat Cummins was all the rave after South Africa, Ryan Harris was considered Australia's best quick and the line hadn't yet been put through experienced and unpredictable left-armer Mitchell Johnson.
However, things have changed in a hurry.
Pattinson has usurped Cummins as the star rookie and, almost overnight, Siddle has gone from struggling to take wickets to white-hot form.
Hilfenhaus has roared back into the Test team after a year-long absence and, as a result, a fit Harris couldn't force his way into the XI for Sydney.
If it weren't for South African seamer Vernon Philander, Pattinson would be hands down the most fearsome fresh blood in Test cricket.
But after starting his career against New Zealand with back-to-back five-wicket hauls, Pattinson's vicious opening in Sydney has brought him even closer to eclipsing Philander's emphatic start.
The 26-year-old Proteas bowler has taken 24 wickets in three Tests at 12.37 and is due to take part in his fourth Test against Sri Lanka on Tuesday night (AEDT).
But Pattinson, five years Philander's junior, has joined the South African on 24 wickets in his fourth Test, at an average of 14.45.
Since Siddle returned from his shoulder injury in the third Test against Sri Lanka in August, he's bowled quicker and his toiling work with the ball is no longer going unrewarded.
Hilfenhaus has reinvented himself as a bowler since he was destroyed by England last Ashes series and subsequently dropped.
The Australian innings started disastrouly, with Dave Warner out for eight and Shaun Marsh a first ball duck - meaning his last four test innings have produced just three runs.
When Ed Cowan was out lbw Zaheer Khan had all three wickets, and Australian were teetering.
But Clarke and Ponting batted sensibly but with attacking intent to put the Indians on the back foot at a ground they have enjoyed individual success in the past.
- With AAP