Scorecard: Australia vs India Teams:
The Indians suffered a huge jolt when Vijay was dismissed for a third-ball duck but Lokesh Rahul (31) and Rohit Sharma (40) ensured that there were no further setbacks till close of play on yet another disappointing day for the visitors.
The second day's highlight was Australian captain Steven Smith notching up his fourth century of the series to join Sir Donald Bradman and Jacques Kallis as only the third batsman to achieve the feat of four successive hundreds in a series.
The young Australian captain, who has been in stupendous form, scored 117 to record his eighth Test ton and put Australia in a commanding position with useful contributions from Shane Watson (81), Shaun Marsh (73) and Joe Burns (58) at the SCG.
Vijay, who has been in good form right through the series, got out to a poor shot off Mitchell Starc. He has scores of 53 and 99 (Adeliade), 144 and 27 (Brisbnane) and 68 and 11 (Melbourne) and his early departure came as a big blow for the Indians.
Earlier, resuming at the overnight score of 348 for two, the hosts rode on a 196-run third wicket partnership between Smith and Watson to take the attack back to the opposition as Mohammed Shami picked up a five-wicket haul.
India though, ably led by Shami (5-112), seemed to have learnt their lessons from the opnening day to concede just 72 runs in 30 overs in the first session of play.
Two wickets fell in the morning session and Watson was the first to go when Shami struck for the second time in the innings to deny the No 3 batsman in what would have been a well-deserved hundred. He added only 20 runs to his overnight score.
Smith played a defiant knock to post his fourth ton in this series only to be caught behind off Umesh Yadav (1-137) in the 114th over of the innings.
But the visitors were once again put to task in the post-lunch when Marsh and Burns managed a 114-run fifth wicket stand to pile on the misery for Virat Kohli and company.
Shami once again picked up the all-important wicket of Marsh, the only wicket for India in the post-lunch session, as the left-hander was caught behind after registering his third Test fifty.
Shami then came back all guns blazing in the final session to send back Burns after the youngster got his maiden Test fifty in just his second match.
Ryan Harris (25) then swung his bat around to hit five boundaries before becoming Shami's fifth strike of the innings.
The Indians, understandably, were more sedate in their reply after losing Vijay and Lokesh and Sharma stitched an unbeaten 71-run stand to raise hopes of revival come day three.
Rohit and Rahul batted with patience for much of the final session of play, with the 50-mark coming in the 19th over. But there were some nerves towards the end as the bowlers searched for one more breakthrough before end of play.
Earlier, Australia had continued their charge towards a high first innings total after tea. Harris, courtesy his 9-ball cameo, helped put up 26 runs for the seventh wicket with Brad Haddin (9 not out) to pile on the misery for India.
Shami then dismissed Harris and the innings was declared. Ashwin (1-142) and Yadav were the other wicket-takers for India, while Bhuvneshwar Kumar (0-122) and Suresh Raina (0-53)
This was after the Smith and Watson show that put Australia on the road to a big score. Post-lunch, Marsh and Burns looked to heap further misery on the visiting bowling attack and they did just that, putting on 114 runs for the 5th wicket without much fuss.
The 450-mark came up for Australia in the 127th over as the two batsmen kept plugging for runs. Marsh brought up his second successive half-century of the series in the 137th over, facing 87 balls. His knock included one six and there were hints of aggression from both batsmen towards the latter half of this second session.
The 500-mark thereafter came up in the 143rd over and an over later they brought up their 100-run stand. In the 146th over, when Burns reached his maiden Test fifty off 94 balls, India became the first team to allow four opposition teams with their top six batsmen all scoring half-centuries in the same innings.
They got some respite when Marsh was out close to the break, caught behind off Shami. But Haddin came out looking to play his shots, hinting that the declaration may come up shortly in the last session on Wednesday.
Australia: Steve Smith (captain), Chris Rogers, David Warner, Shane Watson, Shaun Marsh, Joe Burns, Brad Haddin, Ryan Harris, Mitchell Starc, Josh Hazlewood, Nathan Lyon.
India: Virat Kohli (captain), Murali Vijay, Rohit Sharma Suresh Raina, Ajinkya Rahane, Lokesh Rahul, Wriddhiman Saha, Ravi Ashwin, Mohammed Shami, Umesh Yadav, Bhuvneshwar Kumar.
Scorecard: Australia vs India