Despite the collapse, the tourists hold a 346-run lead with two days to play, and are in prime position to take a 2-1 series lead into the fourth and final test in Sydney.
Rishabh Pant and Mayank Agarwal had a clear plan of getting to a lead of 400 as quickly as possible when they walked out for the start of the day's play and both played their part in pushing the game forward, with Agarwal taking a liking to the spin of Nathan Lyon, hitting two consecutive sixes in one over. It was a poor batting display by the home team's batsmen, who were done in by their own indiscretions rather than the vagaries of the MCG pitch. Marcus Harris (22), who had been struck on his helmet by Bumrah on Thursday, was out top-edging an intended hook to Ishant on the fine-leg boundary.
Jadeja had his first wicket soon after, however, dismissing Harris with a ball pitched into the rough and finding an edge before lodging in Agarwal's mid-riff at short leg.
Oil surges 8% after steep slide; growth fears still weigh
Brent for February settlement dipped $1.39 to $52.43 a barrel on London's ICE Futures Europe exchange. They had fallen 6.2 percent to $50.47 a barrel in the previous session - the lowest since August 2017.
It was just a matter of time for Head's partner Mitchell Marsh (9), whose lean patch with the bat has recently seen him warming the bench more than often and left-arm spinner Ravindra Jadeja took full advantage of his vulnerability.
He left Australia in huge trouble at 89-4 at lunch, trapping Shaun Marsh for 19 with the last ball of the session, a slower full toss that hammered into the lefthander's pads. Travis Head again looked good while making 20, but messed it up by playing all over a reverse-swinging delivery from Bumrah and having his stumps shattered.
With the lead at 392 Kohli appeared to be debating with his vice-captain whether to declare to spare his bowlers the possibility of injury as Cummins continually used the short ball as a weapon.
However, India did not give Australia follow-on. Pant gets a single on first ball. In doing so, Paine and Pat Cummins (17) added 36 runs for the seventh wicket and added some respectability to the total amidst the ruins.