Chasing a MCG record of 340, India crawled to lunch on day five at 3-33, effectively ruling them out of winning the fourth Test.
With the five-Test series locked at 1-1, India only need to draw the series to retain the Border-Gavaskar trophy for a record-extending fifth-straight time.
Mitchell Starc celebrates taking Virat Kohli's wicket late in the first session on day five. (James Ross/AAP PHOTOS)
India openers Yashasvi Jaiswal (14 not out) and Rohit Sharma carefully saw off the first 16 overs until Cummins produced six balls of magic.
Cummins (2-10) removed his opposing skipper, Rohit, with a ball that was juggled and caught by Mitch Marsh.
Five balls later, in-form No.3 KL Rahul fell victim to Cummins for a duck, boosting Australia's hopes of going up 2-1 in the series.
Already in a commanding position, Mitchell Starc removed veteran superstar Virat Kohli (five), who once again was caught behind the wicket.
Starc, Cummins and Scott Boland all regularly bowled deliveries that beat the outside edge on a pitch that is playing more tricks than expected.
Australia added only a further six runs on Monday after they were bowled out for 234 in the second over of day five, giving them a lead of 339.
Nathan Lyon (41) and Scott Boland (15 not out), Australia's No.10 and 11, made 61 in a crucial last-wicket stand that shot the lead past the 300 mark and frustrated India.
Jasprit Bumrah's fifth wicket was an absolute belter! — cricket.com.au (@cricketcomau) #AUSvIND | #DeliveredWithSpeed | @NBN_Australia pic.twitter.com/vfDI5gEN3nDecember 29, 2024
A bumper crowd of more than 50,000 is inside the MCG for what could be a defining day for this generation of Australian players.
A total of 350,700 fans has already attended this Boxing Day Test, breaking the all-time MCG record crowd of 350,534 in the 1936-37 Ashes series, when Sir Don Bradman was king.
The highest successful Test run chase at the ground was nearly a century ago, when England made 7-332 to beat Australia in 1928.
If India win, it will be their third-highest successful Test run chase.
It would even beat the 7-329 they posted to win the fourth Test at the Gabba in 2021 and claim the series.
Australia's recovery from a shaky 6-91 late on Sunday - also helped by Cummins' 41 - was the latest twist in an epic Test full of momentum swings.
India superstar Jasprit Bumrah finished with figures of 5-57, giving him nine wickets for the Test and taking him up to 30 for the series.
More Jasprit Bumrah heroics has given India a chance to win the fourth Test on the final day. (James Ross/AAP PHOTOS)
Australia batsman Marnus Labuschagne, who played in the 2021 loss, said that Brisbane wicket was far removed from the MCG pitch.
Just as Nitish Kumar Reddy and Washington Sundar turned India's fortunes around on Saturday with their epic eighth-wicket stand, Reddy feels one good partnership on Monday will set up India for the win.
Starc noted the absorbing contest was the perfect counter to some commentary that Tests should be shortened to four days.
"This why we've got five days for a Test match and really stick it up those who want four days," he told ABC Radio.
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