Initially, Pujara was circumspect as India stumbled to 6-127 - his first 50 runs came from 153 balls.
Pujara anchored vital partnerships with young wicketkeeper Rishabh Pant and Ravichandran Ashwin before completing his 16th Test century with a flick off his pads after scoring his 5,000th run in Tests.
Pujara, who arrived at the crease after just two overs, waged a heroic battle against Australia's three-pronged pace attack, comprising Mitchell Starc, Josh Hazlewood and Pat Cummins, who had accounted for four of India's top five inside 21 overs, including skipper Virat Kohli, who won the toss and elected to bat first.
Pujara played with the determination and patience lacking from the rest of India's specialist batsmen.
Cummins provided the breakthrough of Ashwin just before the second new ball. All Australian bowlers apart from Travis Head claimed two wickets.
Australia's early aggressiveness was blunted by the heat with the temperature hitting 39 degrees Celsius during the final session, forcing Australia captain Tim Paine to juggle his pacemen with sharp bursts.
The situation got worse when vice-captain Ajinkya Rahane, who signalled his intent by lofting Nathan Lyon for a huge six over long-on, became the fourth Indian player to perish while trying to drive.
Australia took four wickets before lunch with the batsmen guilty of playing at deliveries they would have been better off leaving alone. Instead of middling it, Kohli edged it towards the gully region and Khawaja jumped to his left and plucked the ball one-handed.
The 28-year-old pacer, however, said it is still early days in the Test match and they will need to work hard to achieve a win from here on. He had scored three centuries in his previous two tests in Adelaide. 25-year-old Hanuma Vihar, who made his debut at the Kennington Oval against England, was called up to the 12-member squad, although India chose to field Sharma instead.
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 terrible shot-making and quality Australian pace after captain Virat Kohli won the toss.
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