India, the world's top-ranked nation, are now zeroing in on a first-ever series win Down Under in Sydney later this week, where they only need a draw to smash the long-time jinx.
After India took an unassailable 2-1 series lead, checking the Border-Gavaskar Trophy in for a return journey to India, the best batsman in the world spoke glowingly of the best bowler in the world, at least across formats put together if there are people yet to be convinced of Bumrah's status in each individual format.
They were chasing an unlikely target of 399 but were helped when rain began to fall in Victoria on Sunday morning.
Melbourne Cricket Club CEO Stuart Fox revealed that the MCG is planning to create new pitches, with the aim to have them completed within three years.
Cheteshwar Pujara didn't exactly have a great tour of Australia in 2014-15 but the Saurashtra batsman has been "flexible in altering his game" as per team's demands which has got him success this time, feels skipper Virat Kohli.
"We always believed this is very possible because of the talent that we have in the side", Kohli said.
Top-scorer Cummins will resume on the final day on 61 after a brilliant fighting knock, while Lyon is on six.
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Not one Australian has managed to secure a century so far and tail-ender Pat Cummins's 63 was the highest score by the home side in Melbourne. Lyon added one to his overnight total.
Bumrah's match haul of 8-86 is the best effort by a touring bowler in Australia since Kyle Abbott claimed 9-118 at Bellerive in 2016, when South Africa stormed home by an innings and 80 runs to trigger huge change in Australian cricket.
Bumrah finished with 3-53, following his six-wicket first innings haul, and left-arm spinner Ravindra Jadeja 3-82.
Australia have already named a 13-man squad for the SCG Test, which would suggest Peter Handscomb is the only player in the mix for a call-up for the series finale, but selectors may yet opt for reinforcements.
Earlier, Cummins had taken a career-best 6-27 when India declared their second innings on 106-8 before lunch.
India batted for nearly 170 overs in their first innings on a pitch which remained virtually lifeless during the first two days but went on to deteriorate.
Aaron Finch again flopped - out for three at the top of the order - throwing his role as a Test opener under more scrutiny with the speculation growing that he will now be axed.
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