Pujara's 16th test century saved India after a disastrous start that saw them slump to 86 for five after lunch, falling to a combination of awful shot-making and quality Australian pace after captain Virat Kohli won the toss.
A spectacular catch by Usman Khawaja to dismiss Indian hero Virat Kohli was the highlight of the day for the Australians, while first drop Cheteshwar Pujara proved his mettle for the tourists, scoring a dogged century.
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.
Temperatures in the 40s made bowling an even more daunting prospect, with the Indians' resistance ensuring it was a long day in the field for the hosts.
But the moment of the day came when Pat Cummins entered the attack and Kohli (3) chased the young firebrand's third delivery.
On a day that India's top-order perished due to poor shot selection, Pujara rescued his team with a fighting century.
Five of India's top six were out to loose shots, including captain Kohli, who fell for three to a stunning one-handed catch in the gully by a leaping Usman Khawaja.
Earlier, seamer Josh Hazlewood grabbed two wickets in the morning session, removing Ajinkya Rahane (13) and the out-of-form Lokesh Rahul (two). He found willing support through Ravichandran Ashwin (25) as the pair combined for a 62-run seventh wicket partnership.
Aided by a hint of bounce and movement, Australia's trio of quick bowlers did all the damage in a fiery opening session before Nathan Lyon took over after lunch.
Tail-ender Mohammed Shami survived to stumps on six, with Jasprit Bumrah the last batsman to resume on day two.
Cummins ran, gathered and dived before hurling the ball side-armed from the most hard of angles to end Pujara's excellent ton and the day's play. India would be reasonable happy with the final outcome considering they were 19/3 at one stage.