The hosts were all out for 151 in their first innings. Marcus Harris and skipper Tim Paine were the only locals to offer any resistance. They both made 22 as Jasprit Bumrah rampaged through the batting order.
The 25-year-old claimed six wickets at the cost of 33 runs during an enthralling display of fast bowling.
With a 292 run lead after their own first innings, India could have forced Australia to bat again but India skipper Virat Kohli decided to send his own men out to the crease.
It appeared an unwise ploy as India slumped to 54 for five. Cheteshwar Pujara, who scored a century in the first innings, was out for nought likewise Kohli.
"We wanted to play positive cricket," said Bumrah. "Yes we lost a few more wickets than we wanted but we'll try to add as many runs as we can on the fourth day, then we can come back and try to get them out."
Pat Cummins was Australia's best bowler in India's first innings 443-7 when he took three wickets.
He was as incisive on Friday during India's second innings collecteing four wickets while yielding only 10 runs. "You dare to dream," said Cummins. "It's still a young batting group. They are trying their best and I guess it just didn't come off."
The four Test series is all square at one apiece before the final Test in Sydney which starts on 3 January.