Virat Kohli declared on 622 for seven an hour before the close of play when Ravindra Jadeja was dismissed for 81 and Usman Khawaja (5) and Marcus Harris (19) ushered Australia to stumps on 24 without loss.
The hosts' misfiring attack continued to toil on Friday for scant reward, picking up a wicket in each session, as Pujara extended his most-productive series with a patient 193.
Skipper Virat Kohli finally chose to declare the innings with 622 runs on the board with the loss of seven wickets. Australia won the second test in Perth by 146 runs. And to hold firm against an Indian attack that has picked all 20 wickets in each of the three Tests so far is an even more hard proposition. And that after Australia tried their best to throw them off their lengths with constant, sometimes overdone, use of the feet.
Shaun Marsh (8) edged Ravindra Jadeja to first slip in a tame dismissal that is nearly certain to cast yet more doubt on his Test prospects going forward, and Labuschagne's first innings at first drop ended three overs later when he clipped off his pads and Ajinkya Rahane took a classic catch at mid-wicket. Australian captain Tim Paine is bowled. "Cricket's one of those games, if you keep doing that it can turn really quickly", he said.
Pant had a bit of a scare six runs short of his second test century when he was close to being run out but made his ground safely and reached the milestone off 137 balls with his eighth four - the first Indian wicketkeeper to do so in Australia.
The visitors lead the series 2-1 after winning the opening clash in Adelaide and the third one in Melbourne.
He survived a review decision for caught behind on 12 but was otherwise unmovable.
In a surprise throw of the dice, leg-spinning all-rounder Marnus Labuschagne was called up and will come in at three. "I thought they drove it into us pretty well".
"Pujara was again superb. set the scene for Pant to show his skill".
Lyon (2-116) got the only breakthrough of the session when he had Hanuma Vihari caught to end the 101-run partnership with Pujara mid-way through the session after India resumed this morning at 303-4.
"The team plan was to bat on for as long as possible. we did well", Pant said.