Excluding Australia’s second innings in Adelaide, where Bumrah bowled just six balls, the Indian’s worst bowling figures in an innings this series is 3-42.
The highest successful run chase at the MCG came in 1928 when England reached 7-332 in the fourth innings of a Test against Australia.
No team has scored more than 261 in the fourth innings of a match in Melbourne since the MCG renovated its drop-in pitches in 2018.
India will know they blew a chance to take the upper hand when the home side had slumped to 6-91.
Bumrah became the first man in Test history to take 200 wickets at an average of under 20 as Australia collapsed on the fourth day of the fourth Test, putting a dent in their hopes of a series win.
Moving along steadily at 2-80 and with a 185-run lead midway through the day, Australia lost 3-4 in 10 balls.
India had started the day at $7.50 with bookmakers but rocketed into favouritism at one stage.
Sam Konstas, fresh off an entertaining 60 in the first innings, made just eight.
From the outset, India put men back at third man and fine leg to nullify the risk of Konstas playing ramp shots. The NSW opener was then on the receiving end of a beautiful ball from Bumrah that seamed back in and cannoned into his middle stump.
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Usman Khawaja was then bowled for 21 before Steve Smith (13) edged a wider ball outside the off stump.
Head, the leading run-scorer in this series who made a duck on day one, was out for one in the second innings.
Mitch Marsh’s horror run also continued with a sixth single-digit score from seven visits to the crease this series. Before the third Test in Brisbane, Marsh was the only member of Australia’s top seven who hadn’t been dismissed by Bumrah. He joked at a press conference that his time was coming.
It certainly was, with Bumrah now having dismissed Marsh in three of his last four innings.
Bumrah picked up his third wicket in 11 balls by bowling Alex Carey.