Despite more batting failures Australia were still alive at stumps on 258 for eight, needing another 141 runs with the gutsy Cummins not out 61, while India just two wickets away.
Melbourne: Australia were teetering on the brink of defeat in the third Test on Saturday despite a battling unbeaten half century from tailender Pat Cummins after being set a massive 399 to win by India.
After early morning drizzle, India started an overcast fourth day in Melbourne with a 346-run lead and with five wickets in hand on a wearing pitch becoming increasingly difficult to bat on.
Skipper Virat Kohli declared at 106 for eight, leaving Australia to chase what would be a record fourth innings total of 399 at the Melbourne Cricket Ground.
The previous biggest successful run chase at the ground came in 1928, when England made 332 for seven.
Despite more batting failures Australia were still alive at stumps on 258 for eight, needing another 141 runs with the gutsy Cummins not out 61 – only his second Test 50 and his highest ever score. It followed his career-best 6-27 with the ball.
He was accompanied by Nathan Lyon, who was not out on six, in the rearguard action.
India still have a day in hand to wrap up the last two wickets as they zero in on a first-ever series win Down Under. There is just the Sydney Test next week to go, with the series level at 1-1.
Australia's task was made harder when Aaron Finch again flopped, throwing his role as a Test opener under ever more scrutiny with speculation that he either has to drop down the order in Sydney or make way for someone else.
He played a poor shot to pace spearhead Jasprit Bumrah – who snared six wickets in the first innings – and was caught by Kohli for three.
Fellow opener Marcus Harris followed him back to the pavilion for 13, getting an inside edge from spinner Ravindra Jadeja to Mayank Agarwal close in.
Usman Khawaja was the next to go after a lively 33, trapped lbw by Mohammed Shami. He chose to review the decision with the ball-tracking technology showing it clearly hitting the off stump.
When Shaun Marsh was also trapped leg before by Bumrah for a brisk 44 and his brother Mitch – another candidate for the Sydney axe – fell for 10, Australia's faint survival hopes were fading fast.
Travis Head put up some resistance with a battling 34 before his stumps were knocked over by Ishant Sharma and when skipper Tim Paine went for 26 it appeared all but over – until Cummins dug in.
Cummins had brought the game back to life late Friday by grabbing four wickets in a devastating spell after his team were skittled for just 151 in reply to India's first innings 443 for seven declared.
Debutant opener Agarwal, who had witnessed the carnage from the other end, showed early aggression on Saturday when they resumed, rushing down the pitch to smack spinner Nathan Lyon for two big sixes.
But he was no match for Cummins who was again Australia's saviour when a low delivery ricocheted off the bat onto the stumps and he was out for 42.
It was Cummins' third five-wicket haul in his 17 Tests -- and he achieved the feat in just nine overs for 14 runs.
Not satisfied, he then had Jadeja caught at short point by Khawaja for five to give him career-best figures of 6-27 off 11 overs.
When Rishabh Pant fell to Josh Hazlewood for 33, Kohli made the declaration.
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