The Indian pace sensation instigated a collapse of 4-11 in 21 balls at the MCG on Sunday, leaving Australia delicately poised on 6-135 at tea on day four.
Australia's lead has grown to 240 after taking a 105-run advantage into their second innings when they bowled India out for 369 17 minutes into the first session of the day.
Marnus Labuschagne (65no), who had a life on 46 when Yashasvi Jaiswal dropped his second of three catches of the day, is anchoring the Australian innings, with captain Pat Cummins (21no) hanging in for support.
India's bowling strategy on Sunday was clear - attack the stumps.
During a frantic three-over spell after lunch, Bumrah claimed the wickets of Travis Head (1), Mitch Marsh (0) and Alex Carey (2), giving him figures for that period of 3-4.
The dismissal of Head, a soft catch to square leg, was Bumrah's 200th Test wicket.
The 31-year-old reached the 200-wicket milestone with a better career average - 19.56 - than any bowler in history.
Bumrah has 29 of the 63 wickets India has taken during this Border-Gavaskar series at a measly average of 12.34.
Before lunch, Bumrah exacted revenge on Sam Konstas for the teenage debutant's Boxing Day ramp-fest.
Veteran opener Usman Khawaja avoided falling victim to Bumrah for the sixth time in the series.
Usman Khawaja couldn't capiitalise on his start, bowled by Mohammed Siraj for 21. (James Ross/AAP PHOTOS)
But when Khawaja (21) was looking set, the left-hander was bowled by Mohammed Siraj, who shushed the crowd, with Australian fans booing him since he gave Travis Head a send-off in Adelaide.
After writing himself into Boxing Day folklore with an audacious 60 on Thursday, Konstas was out for eight in his second Test innings when Bumrah rattled his stumps.
The 19-year-old has enjoyed every minute of his Test debut, interacting with the crowd, and taking selfies with spectators.
When Bumrah dismissed Konstas, the world's No.1 Test bowler threw his hands up in the air to the strong Indian contingent sitting in the Ponsford Stand.
The 31-year-old's celebration seemed to mimic what Konstas had been doing with the crowd while fielding.
A brilliant maiden century from Nitish Kumar Reddy powered India past the follow-on target on Saturday, after the tourists were in trouble at 5-164 in reply to Australia's 474.
Nathan Lyon removed century-maker Nitish Kumar Reddy, finishing the innings with 3-96. (James Ross/AAP PHOTOS)
Reddy, just 21 and playing in his fourth Test, helped India add another 11 runs to their overnight score of 9-358.
Scott Boland was the pick of Australia's bowlers with 3-57 from 27 overs.
Australia bowled 120 overs at India as the effects of a gruelling series appear to take their toll on Mitchell Starc.
The star quick received treatment on his back on day three, but continued to bowl at top pace for Saturday's final session.
Starc has toiled for 25 overs in this Test, backing up from the 24 he bowled in Brisbane.
Mitchell Starc appeared to show the effects of a tough campaign on Saturday. (James Ross/AAP PHOTOS)
Boland was recalled to the XI after star quick Josh Hazlewood broke down for a second time in the series at the Gabba.
The fitness of Australia's bowling attack will be a major factor in deciding the outcome of the Border-Gavaskar trophy.
This Test is set to go five days, a rarity in modern cricket in Australia, meaning the players will have only three days off before the finale at the SCG gets underway.
With the five-match series tied 1-1, India will retain the Border-Gavaskar trophy if they pull off an extraordinary comeback victory in this Test.
Reserve batter Josh Inglis has been ruled out for the rest of the series after suffering a calf strain while fielding on day two.
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