Middle-order batsman was unbeaten on 130 runs at close of play on day one
Irrepressible Cheteshwar Pujara stroked his third century of the summer Thursday to put India in a commanding position in the decisive fourth and final Test Thursday as they strive for an historic series win in Australia.
At stumps on day one, they were 303 for four with the rock-like number three not out 130 and Hanuma Vihari on 39. Mayank Agarwal made 77 with Josh Hazlewood the best of the bowlers with 2-51.
After toiling on a hot Sydney day, Australia were rewarded with the wickets of KL Rahul, Agarwal, Virat Kohli and Ajinkya Rahane, but despite a five-pronged attack the key scalp of Pujara remained elusive.
The visitors lead the series 2-1 after winning the opening clash in Adelaide and the third one in Melbourne. Australia claimed victory in Perth.
If India, the world's top-ranked nation, win or draw in Sydney they will clinch a first-ever series in Australia since they began touring Down Under in 1947-48.
Kohli again won the toss with Rahul back in the team to open with Agarwal and Vihari dropping to number six to cover for the unavailable Rohit Sharma.
Australia got an early breakthrough with Josh Hazlewood tempting Rahul into a defensive shot that took a outside edge and carried to Shaun Marsh at first slip, and he was gone for nine.
But that only brought the stoic Pujara to the crease and like he has done all series, the 68-Test veteran dug in and blunted the new ball.
He survived a review decision for caught behind on 12, but otherwise gave a masterclass, brushing off two nasty hits to the shoulder.
In another innings of patience and concentration, he slowly picked off runs to bring up his 18th Test century from 199 balls, with 13 boundaries.
The methodical 30-year-old has been by far the best batsman from either side across the series and his ton followed a stellar 123 in the first Test in Adelaide and 106 in the third Test at Melbourne.
Playing in only his second Test, the Bangalore-born Agarwal was also impressive.
He was targeted with bouncers and struck on the helmet but held firm, reinforcing his credentials after a solid debut in Melbourne.
He worked hard to make his second Test 50 in only three innings by caressing a Mitchell Starc delivery through the covers for four.
But he began to open up with the bat and after hitting Nathan Lyon for six to bring up his highest Test score of 77, attempted to do the same from the next delivery and was caught by Starc at long-on.
Master batsman Kohli was welcomed by boos from a section of the crowd and immediately silenced them with an exquisite four off Hazlewood.
But after a restrained 23 Hazlewood snared him in the first over after tea when a leg-side delivery flicked off his glove to Tim Paine behind the stumps.
Vice-captain Ajinkya Rahane looked good in making his way to 18, but a Starc bouncer caught him off guard and it too caught his glove for Paine to take an overhead catch.
For Paine, it was the sixth toss he had lost in seven Tests and it could prove costly on a Sydney Cricket Ground pitch expected to be conducive to spin as it wears.
When Australia bat, they will have a new look opening pair with Usman Khawaja padding up with Marcus Harris after the underperforming Aaron Finch was axed.
In a surprise throw of the dice, leg-spinning all-rounder Marnus Labuschagne was called up and will come in at three.
Mitch Marsh was also dropped with Peter Handscomb back to counter India's two spinners — Kuldeep Yadav and Ravindra Jadeja.