Australia lost David Warner early but reached tea at 38 for one after dismissing India for 475 and a 97-run first innings lead on the fourth day of the fourth test on Friday.
Warner had come out in typical combative style and already had four runs on the board when he was caught in the slips off spinner Ravichandran Ashwin, who had taken the new ball.
Shane Watson would have joined him had India's fielding been sharp enough to take a run out chance but he survived to reach the break on 13 not out alongside opener Chris Rogers, who had set the pace with an unbeaten 21.
The Australians, who lead the series 2-0 and had made 572-7 declared in their first innings, struck early to remove Virat Kohli and winkled out four more batsman despite the Sydney Cricket Ground still offering excellent batting conditions.
Kohli clipped a Ryan Harris delivery to Rogers at midwicket after having added just seven runs to his overnight score.
The skipper's 147 helped bring his tally over the four tests to 646 runs, the second highest by an Indian batsman in an overseas series after the 774 Sunil Gavaskar accumulated in West Indies in 1971.
The hosts got some help from the third umpire to get rid of Bhuvaneshwar Kumar from a referred decision that will do little to persuade India to embrace the Decision Review System.
Kumar had survived a couple of close calls off the bowling of Nathan Lyon and reached 30 in a doughty 65-run partnership with Ashwin before the Australian off-spinner controversially got his man.
The batsman certainly made contact with the Lyon delivery, the ball coming off the bottom of his bat in a spray of dirt and flying to Watson in the slips.
After a muted appeal from the Australians, the officials referred the decision to the third umpire who, to the disbelief of almost everybody in the ground, decided he was 100 per cent certain the ball had come straight off the bat to Watson.
Mohammed Shami (16) suffered a examination from Mitchell Starc but the next wicket to fall was that of Ashwin, who had just reached his half century when he was caught behind off the left-armed paceman and the end of the innings was in sight.