Despite a tail-end collapse in which the hosts lost five wickets for just 19 runs as they finished their first innings on 503, India were still in command but not as authoritative as it could possibly have been.
However, Ravichandran Ashwin claimed the wickets of David Warner and Phil Hughes - both batsman playing naive shots - as the tourists finished the day on 74 for two..
Australia were moving steadily along in their reply with Ed Cowan and Warner looking well-set before the latter was removed by Ashwin with the score on 56.
The Australian attempted a sweep but missed the ball which in turn went through to hit the leg stump.
There had been no further scoring when Ashwin took his second wicket of the day, again to a delivery tossed up outside leg.
Hughes looked to sweep but the ball hit him on the glove and rolled back on to the stumps.
Both dismissals displayed an alarming lack of technique, the batsmen attempting scoring shots rather than padding the ball away with no risk of being out leg before wicket.
Australia resisted further damage, digging in to end the day with Cowan and Shane Watson unbeaten on 26 and nine respectively.
The hosts were put in a position of strength thanks largely to Cheteshwar Pujara's 204.
However, they then suffered a collapse that included the loss of four wickets for seven runs to end on 503 all out with Glenn Maxwell finishing with four for 127.
Maxwell claimed his first Test wicket, Murali Vijay caught by Cowan at leg slip to end a partnership of 370 with Pujara - India's fourth-highest for any wicket.
The crowd roared to welcome Sachin Tendulkar to the crease, and he was on hand to congratulate Pujara when he advanced down the wicket to hit Maxwell for four and reach 200 for the second time in Test cricket.
Soon the Australian fielders were congratulating him too as he walked off the field having been caught in the deep by Xavier Doherty when he aimed a hook shot at a James Pattinson bouncer but could not keep it down.
After returning from lunch at 400 for three, the hosts had only added four more runs when Tendulkar was contentiously out for just seven.
The third umpire ruled the India legend had got a touch on a Pattinson delivery which then went through to wicketkeeper Matthew Wade.
Australia made a further breakthrough when they took the wicket of captain Mahendra Singh Dhoni after a quickfire 44.
Dhoni fired a fierce shot off a Maxwell delivery which did not have the required height and was taken by Doherty at mid-off - although he required two attempts at grabbing the ball.
Dhoni's 44 came off 43 deliveries and included eight boundaries.
Maxwell then enjoyed more success when he removed Ravindra Jadeja caught and bowled, and Australia made further inroads with just one more run scored with spinner Doherty taking out Ashwin, caught at gully by Hughes having made just one.
Harbhajan Singh became Doherty's second victim with four more on the board when he hit a ball straight to Maxwell to go for a duck.
India's tail continued to crumble with Virat Kohli the next to go when he got an inside edge to a Maxwell delivery and Cowan dived to his left to pluck the ball out of the air.
Kohli had made a patient 34 off 92 balls.
India's innings was then brought to an end when Bhuvneshwar Kumar was stumped for 10.