Marcus Harris was five not out, with Aaron Finch on three as Australia started their response to India's 443 for seven total, with the home bowlers made to toil until half an hour before stumps on a grudging Melbourne Cricket Ground (MCG) wicket.
In a brief and fiery spell, paceman Jasprit Bumrah struck Harris on the helmet with a short ball but the rookie opener rose to his feet quickly and resumed after lengthy attention by medical staff.
With the four-test series locked at 1-1, much will depend on how the MCG's maligned drop-in wicket performs for an Australian batting order still finding their feet.
But the home side's hopes of taking a lead into the final test in Sydney would seem slender.
Although they failed to make a breakthrough, India's bowlers will head into day three hopeful of making some early inroads after they beat the bat with a slew of deliveries, but Finch feels all three possible results remain on the table.
"We've very confident we can bat really big, bat well and put India under pressure again," he told reporters. "This wicket is deteriorating a lot more than probably what we thought it would."
Having gone to stumps at 215-2 on day one, India's batsmen enjoyed another dominant day, with an obdurate Pujara scoring his second century of the series and skipper Virat Kohli adding 82 in a steady 170-run partnership.
Rohit Sharma, back in the side after missing the second test in Perth through injury, also contributed an unbeaten 63 before Kohli declared following Ravindra Jadeja's caught-behind dismissal for four.
India's cause was given a huge help by their opponents' sloppy fielding, with Australia grassing two catches under a blazing sun to reprieve Rohit and wicketkeeper Rishabh Pant (39).
The tourists' batsmen had little trouble dealing with spinner Nathan Lyon, who had to wait until after tea to grab his first wicket when he trapped Ajinkya Rahane plum in front for 34.
Earlier, pace spearhead Mitchell Starc denied Kohli a second century of the series when he had him caught ramping to third man before Pat Cummins bowled Pujara for 106, after the watchful batsman registered his 17th test ton.
Pujara, who scored a match-winning 123 in the series-opener in Adelaide, was removed by a virtually unplayable delivery that kept low and nipped back off the seam to clip off-stump.
"I don't think it's easier to bat now," he said. "So from tomorrow onwards, I think it will get difficult to bat and our bowlers have been bowling well."
(Reporting by Ian Ransom; Editing by Greg Stutchbury/John O'Brien)
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