Jasprit Bumrah, standing in for Rohit as skipper, won the toss and decided to bat despite the leaden skies and a wicket with a distinct tinge of green.
KL Rahul and Yashasvi Jaiswal both departed cheaply early on and Shubman Gill, Rohit's batting replacement, was caught in the slips for 20 off Nathan Lyon to bring up lunch.
Virat Kohli survived a big scare on the first delivery he faced in a moment of high drama.
Fast bowler Scott Boland thought he had Kohli out for a golden duck but the roars of the sellout crowd turned to jeers when the third umpire ruled the ball had kissed the grass before slip fielder Steve Smith flicked it up for Marnus Labuschagne to catch.
Boland ended up dismissing Kohli for 17.
At tea Rishabh Pant was on 32 and Ravindra Jadeja was on 11.
Australia lead the series 2-1 after rebounding from a thrashing in the Perth opener to win the tests in Adelaide and Melbourne, which sandwiched a draw in Brisbane.
The tourists need a win in the series finale to retain the Border-Gavaskar Trophy.
Bumrah attempted to douse rumours of rifts in the India camp when he said Rohit's absence from the team was the out-of-form 37-year-old's own choice.
"Our captain has shown leadership by opting to rest in this game," he said at the toss.
"That shows there's a lot of unity in this team. There's no selfishness. Whatever is in the team's best interest, we are looking to do that."
-Reuters