Pujara (109 not out) and new man Karun Nair (13 not out) were at the crease when the umpires signalled the end of the second session, which witnessed the fall of skipper Virat Kohli (6) and Ajinkya Rahane (14).
Resuming the session at 193/2, Pujara switched gears to bring up his 50 off 155 deliveries with Kohli, who defied his shoulder injury and came out to bat at his regular No.4 spot.
Forced to leave the ground in the 40th over on the opening day, Kohli spent the rest of the first day and the whole of second day in the dressing room getting medical attention from the support staff.
He had undergone scans on Thursday night, prompting some media reports which said he had been ruled out of the Test.
However, the 28-year-old's stay at the crease was not long as he was out for six after being caught by his opposite number Steve Smith at second slip off pacer Pat Cummins.
Next in, Rahane looked good during his brief stay but failed to repeat the kind of partnership which he and Pujara displayed to save the second Test in Bengaluru.
Rahane looked positive from the start, consuming 33 deliveries and added 51 runs for the fourth wicket before being caught behind by wicketkeeper Matthew Wade off a bouncer from Cummins to leave India in a spot of bother.
The loss of two crucial wickets at the other end, however, did not deter Pujara to play his shots as he got to his next 50 runs in just 59 deliveries.
Thereafter, Nair joined Pujara in the middle and the right-handed duo ensured India went into the break without any more casualities.
Earlier in the first session, opener Murali Vijay (82) and Pujara dug deep and played with poise to help India post 193/2 in reply to Australia's 451 at lunch.
The duo, known to play copybook shots in the longest format of the game, stitched together a 102-run stand for the second wicket after the hosts had lost a set opener Lokesh Rahul (67 off 102 balls) towards the end of the second day.
Left-arm spinner Steve O'Keefe (1/67) gave the Aussies something to cheer about in the last ball of the first session, taking the wicket of Vijay (82 off 183) who played for spin but was stumped by wicketkeeper Mathew Wade.
For the visitors, Cummins was the most successful bowler with figures of 3/49 while O'Keefe took the lone wicket of Vijay.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)