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.
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.
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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.
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.