Cheteshwar Pujara faced 246 balls in his gutsy knock - passing 5,000 Test runs for his 16th Test century.
Adelaide - Nathan Lyon, Pat Cummins, Josh Hazlewood and Mitchell Starc all grabbed two wickets
Cheteshwar Pujara scored a gritty 123 in punishing conditions to claw India back into the opening Test in Adelaide Thursday after Australia seized early control with some blistering bowling.
Nathan Lyon, Pat Cummins, Josh Hazlewood and Mitchell Starc all grabbed two wickets as temperatures topped 36 Celsius (96.8 Fahrenheit) and the tourists wilted to 250-9 at stumps on day one.
The experienced Pujara faced 246 balls in his gutsy knock - passing 5,000 Test runs for his 16th Test century - as the wickets tumbled around him, including superstar captain Virat Kohli for three.
At the end of a day characterised by poor shot selection, Pujara went for a quick single on the second last ball and was removed in a brilliant run-out by a diving Cummins.
"It was one of my top innings in Test cricket, I could say top five," said Pujara, adding that he was disappointed other batsmen didn't do as well.
"To be honest we should have batted better but they also bowled well in the first two sessions and I knew that I had to stay patient and wait for the loose balls.
"We'll learn from the mistakes and put up a better show in the second innings."
Batting after Kohli won the toss, the visitors crumbled in a disastrous morning session under a pace barrage before digging in later in the day, with Pujara and Ravi Ashwin (25 off 76 balls) staging a fightback as the bowlers tired.
In their first home Test since the ball-tampering scandal in March, Australia took four wickets before lunch with the batsmen guilty of playing at deliveries they would have been better off leaving alone.
Australian bowling coach David Saker said it was a premeditated plan for the quicks to pitch it up and lure India's batsmen into false shots.
"We got the wickets the way we thought we might get the wickets," he told the Seven Network.
Starc added that he felt the attack was excellent for much of the day, but they let it slip in the final hour. But he was happy overall.
"If you'd said to us at the beginning of the day after losing the toss that we have them at 250-9, we'd have bitten your arm off," he said.
Opener KL Rahul, who has been struggling for runs, flopped again, caught by Aaron Finch at third slip off Hazlewood for two.
Veteran Murali Vijay, in the side after young gun Prithvi Shaw suffered ankle ligament damage, didn't last much longer, caught behind by skipper Tim Paine off Starc for 11.
In marched Kohli to a huge roar from the crowd, but Usman Khawaja at gully spectacularly caught him off a Cummins delivery as he attempted a drive, out after facing only 16 balls.
It was stunning one-handed take by Khawaja, whose preparations were upset by the shock arrest of his brother this week for allegedly framing a love-rival with a fake terror plot.
The dismissal of Kohli, who has scored five centuries in his two previous Test tours of Australia and rates Adelaide his favourite overseas ground, sparked wild celebrations.
Vice captain Ajinkya Rahane and Pujara worked to steady the ship.
But after returning from a break, Hazlewood enticed Rahane into a drive and he edged to Handscomb in the slips for 13.
Rohit Sharma, preferred in the final XI to all-rounder Hanuma Vihari, had compiled a patient 31 when he swept Lyon for six, narrowly missing being caught on the ropes.
Sharma then needlessly tried the same shot on the next ball, and this time debutant Marcus Harris comfortably collected the steepling catch, with the right-hander once more failing to capitalise on a good start.
It was left to Pujara, in his 65th Test, to stay at the crease and keep chipping away, building a 41-run partnership with Rishabh Pant and then 62 with Ashwin before he was run out by Cummins.
Indias 290 for 9
India first inningsM. Vijay c Paine b Starc 11
KL. Rahul c Finch b Hazlewood 2
C. Pujara run out (Cummins) 123
V. Kohli c Khawaja b Cummins 3
A. Rahane c Handscomb b Hazlewood 13
R. Sharma c Harris b Lyon 37
R. Pant c Paine b Lyon 25
R. Ashwin c Handscomb b Cummins 25
I. Sharma b Starc 4
M. Shami not out 6
Extras (lb1) 1
Total (9 wickets, 87.5 overs) 250To bat: Jasprit Bumrah
Fall : 1-3 (Rahul), 2-15 (Vijay), 3-19 (Kohli), 4-41 (Rahane), 5-86 (Sharma), 6-127 (Pant), 7-189 (Ashwin), 8-210 (Sharma), 9-250 (Pujara)
Bowling: Starc 19-4-63-2, Hazlewood 19.5-3-52-2, Cummins 19-3-49-2, Lyon 28-2-83-2, Head 2-1-2-0
Australia:Marcus Harris, Aaron Finch, Usman Khawaja, Shaun Marsh, Travis Head, Peter Handscomb, Tim Paine (capt), Josh Hazlewood, Pat Cummins, Nathan Lyon, Mitchell Starc
Umpires: Nigel Llong (ENG), Kumar Dharmasena (SRI)
TV umpire: Chris Gaffaney (NZL)
Match referee: Ranjan Madugalle (SRI)