Previously, Farukh Engineer, with a score of 89 at an Adelaide Test, had the highest score for an Indian wicket-keeper in Australia.
Pujara came up seven runs short of his fourth double century but there can be little doubt that his nine-hour, 373-ball knock will nearly certainly deliver India's first Test series victory in Australia.
Earlier, Lyon (4-178) got the only breakthrough of the morning session when he had Hanuma Vihari caught to end the 101-run partnership with Pujara midway through the session after India resumed this morning at 303-4.
At the interval, Pujara was 181 not out with Rishabh Pant unbeaten on 27, sharing a 60-run partnership at the Sydney Cricket Ground as India continued its tried and tested approach this series of building successive partnerships to grind Australia's bowling attack down. Jason provides us with a left arm option in the absence of Mitchell Starc and is very capable of taking wickets early in the innings.
It was left to Handscomb, recalled as a specialist in tackling spin, and paceman Cummins, who made a gutsy 63 in the third Melbourne Test, to try and fix the damage.
Since the end of the series against Pakistan on Australia Day, 2017, Australia have lost 18 of 21 completed ODIs. Kuldeep did not stop there. Australian captain Tim Paine is bowled.More news: Maurizio Sarri: Chelsea Need 'Something Different' At Striker
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OUT! Just when things started to look good for Australia, Kuldeep Yadav has struck. Harris had taken up the challenge and moved step by step to lay the foundations for a big inning.
In the time since leaving that tour following the Lord's Test, Kuldeep has taken 10 wickets in two home Tests against West Indies and gone back to his childhood coach, Kapil Dev Pandey, in a bid to get back to the basics of his craft.
Channelling the man he resembles when batting, David Warner, Harris did not let the bowlers stifle him. But despite the hosts having a tough first session, Rahul was quick to signal that he has not finished the catch and the ball has taken a bounce before he caught it. Instead, he lobbed the ball back into the spinner's hands. There is a real lack of confidence within the batting group.
Shami was hit out of the attack with two fours in one over, and then Harris used his feet to crash Jadeja through the covers. With Khawaja helping set the tone by skipping out to Jadeja over mid-off and reverse-sweep with authority, Australia scored 31 runs between the 15th and 19th overs.
Labuschagne scored 38, showing promise but ultimately failing to cash in after his contentious call-up.
Having fielded for nearly two full days, Australia navigated a tricky 10-over spell late in the day via Marcus Harris (19 not out) and Usman Khawaja (5no) to reach 24-0 at stumps, still trailing by 598 runs, albeit fortuitously after Khawaja was dropped by Pant. Usman Khawaja, not trusting his defence enough against Kuldeep, jumped down the track to try and slog over midwicket, but the ball dipped on him, he failed to get to the pitch and found the fielder inside the circle.