But Pujara stood tall amid the ruins to take India to 250/9 at stumps.
It was his third ton against Australia but first in Australia, and the innings only ended on 123 thanks to a sensational diving run out from Pat Cummins, which brought an end to the day's play.
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 exhausted.
"I thought we bowled really well for four hours, probably pretty well for another hour and probably got it a bit wrong at the end there", Starc told reporters.
KL Rahul edged Josh Hazlewood to Aaron Finch at slip for two as his struggle for runs continued, with fellow opener Murali Vijay (11) following shortly caught by Australia skipper Tim Paine off the bowling of Mitchell Starc to leave the tourists 15-2.
But after eight months of soul-searching and scathing criticism, there was lot for disillusioned fans and Paine to like as his side finally started their first home Test since the Cape Town cheating scandal and first match on free-to-air TV this season.
Pujara faced 141 balls for a dogged 46 not out with his latest partner Ravi Ashwin unbeaten on five on a day characterised by poor shot selection. "We've had a good day but we know that one good day will not win a series".
That is, until he attempted a quick single on Cummins' arm.
Vice-captain Rahane (13) was then enticed into a drive with Peter Handscomb taking the catch in the slips as India lost their fourth wicket before lunch.
Rohit Sharma, preferred in the final XI to all-rounder Hanuma Vihari, compiled a patient 31 before sweeping Lyon for six, narrowly missing being caught on the ropes.