Pacer Mitchell Starc struck twice at the start of the innings and Josh Hazlewood once to leave India reeling at 22 for three at lunch after Australia racked up 445 in their first innings.
Starc removed Yashasvi Jaiswal in the second ball of the India innings and then dismissed Shubman Gill before Hazlewood got prized wicket of Virat Kohli as the visitors stared down the barrel of another poor outing with the bat after their failures in Adelaide.
Jaiswal was out caught by Mitchell Marsh at short midwicket while he tried to clip a Starc half-volley off his pads.
Gill was sent back when Marsh pulled off a brilliant catch in the slip cordon off the bowling of Starc after the India number three played away from the body.
Kohli was dismissed in what has now become a familiar scene as he once again chased a length delivery outside off before nicking it to Alex Carey.
Rishabh Pant was also caught behind off Pat Cummins trying to push the ball away from his body. KL Rahul (33 not out) and Rohit Sharma (zero not out) were at the crease.
Earlier, Australia ended the innings at 445 all out, riding on centuries from Travis Head and Steve Smith. Wicket-keeper Alex Carey provided quick runs batting with the tail on Day 3 before falling for 70. Bumrah finished with 6/76.