Kohli and Rahul hundreds lift India
India 5 for 342 (Kohli 140*, Rahul 110, Rohit 53) trail Australia 7 for 572 dec by 230 runs
Scorecard and ball-by-ball details
It is hard to decide what was more predictable on a belter of a Sydney pitch, the Steven Smith century that was raised on day two or the Virat Kohli hundred that arrived on day three. They now have four centuries each for the series, and are duelling for records. Much less expected was a maiden Test ton from KL Rahul, whose debut in Melbourne was memorable for all the wrong reasons.
The third day at the SCG was much the same as the first two, terrific for batting and full of toil and despondency for the bowling side. Australia managed four wickets for the day, including two in two balls from Shane Watson after tea, but India added 271 runs to their total and by stumps were 5 for 342. Kohli was on 140, Wriddhiman Saha had 14, the deficit was 230, and a draw was the favourite.
Of course, with two days to play Australia could yet run through India's tail, or sporting declarations could make a game of it. But a total of 12 wickets from the first three days of play was an indication of the true nature of the surface. Kohli and Rahul enjoyed it most of the Indian batsman, although Rohit Sharma also managed a half-century on his return to the side.
The key partnership for India was the 141-run third-wicket stand between Rahul and Kohli. Together they steered India untroubled through the second session, and lifted the scoring tempo following a tepid first session in which dot balls piled up and only 51 runs were scored. If it was slow, it was at least solid, and gave India the platform they required.
A slipshod fielding effort from the Australians helped India - Smith put down two catches and a run-out chance was missed when a substitute fielder threw to the wrong end. But the batsmen made the most of their opportunities and scored all around the wicket. Kohli's hundred came from his 162nd delivery with a push past the bowler Josh Hazlewood for two, and it continued a remarkable series.
Kohli became the third visiting batsman after Herbert Sutcliffe and Wally Hammond to score four centuries in a Test series in Australia, and later he went past Rahul Dravid's 619 in the 2003-04 series in Australia for the most runs by an Indian in a Border-Gavaskar Trophy series. Both he and Smith remain in the hunt to break Don Bradman's all-time record of 715 runs in an Australia-India series.
Kohli struck 20 fours and was especially strong driving through the off side and pulling anything short, but really there was almost no weakness in his game. He did give a chance on 59 when he edged the second new ball to second slip off Mitchell Starc, and was fortunate that it burst through the hands of Smith above his head.
Kohli's first ball had been eventful - he pushed at Lyon and the ball ricocheted off Brad Haddin's thigh, and Rahul wanted a run. He was turned back, but the substitute fielder threw to Haddin instead of the bowler. Smith was frustrated at that lapse, which could have ended Rahul's innings, and it was far from the only frustration for the Australians throughout the day.
Smith gave Rahul a life before lunch when on 46 he top-edged a pull off Watson and Smith running back from slip appeared distracted by SpiderCam and put down the chance. Rahul then brought up his half-century from his 161st delivery with a boundary through extra cover off Lyon.
Like Kohli, Rahul was impressive when pulling the spinners but mostly when finding the gaps through the off side. Nine of his 13 boundaries came in the region from backward point to extra cover, and his century came in the final over before tea when he steered a Starc delivery behind point for a boundary from his 253rd ball.
Having been out slogging across the line batting down the order in both innings in Melbourne, this was a chance to prove himself in the more familiar opening role, and he did not disappoint. Eventually, Rahul fell for 110 when he skied a top-edged pull off Starc and the bowler did well to avoid colliding with the batsman and take the return catch.
It was the first of three wickets for Australia in the final session. Ajinkya Rahane was unlucky to be given out lbw to a Watson delivery that would have gone over the top, and next ball Suresh Raina's long-awaited return Test innings ended first delivery when he edged a fullish ball behind to Brad Haddin. Watson missed the hat-trick but for the first time since the 47 all out Cape Town Test of 2011, he had taken more than one wicket in a Test innings.
It meant Australia had four wickets for the day after Nathan Lyon claimed Rohit in the first session. Rohit's half-century had come from his 132nd delivery when he drove a boundary through cover off Ryan Harris, but on 53 he tried to sweep Lyon from outside off and his under-edge deflected back onto the stumps.
Although Lyon was the only wicket-taker in the first session, the pressure built by the other Australian bowlers was generally excellent. Collectively the Australians bowled 157 dot balls during the session and India had 22 scoring shots. By the end of the day, they had many, many more.
Brydon Coverdale is an assistant editor at ESPNcricinfo. @brydoncoverdale