Bumrah's skipper is confident that his men won't take their feet off the pedal and win the series 3-1.
In contrast, India were disciplined with rock solid number three Cheteshwar Pujara scoring another century and Kohli showing restraint and composure, while debutant Mayank Agarwal impressed at the top of the order with 76 in his first Test knock.
Pat Cummins (63) and Nathan Lyon (7) were dismissed as Australia fell for 261, well short of their target of 399.
In the fourth innings, India once again struck early and all the bowlers got into the act to set up a memorable victory.
In fact, Kohli would have been anxious when rain did not allow a single delivery to be bowled in the first session of the fifth day.
AUSTRALIA captain Tim Paine has been left frustrated by the pitches rolled out for the Border-Gavaskar Test series, declaring that the decks have worked against the hosts. "Whether it's the system ... whether it's something we've got to change in our psyche, I'm not sure".
With all-rounder Mitchell Marsh and opener Aaron Finch being doubtful to retain their spots for the final Test, Paine also confirmed that there would be "a lot of things on the table" when the team selectors meet in Sydney.
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India won the first Test in Adelaide by 31 runs with Australia bouncing back to claim the second in Perth by 146 runs. We bowl a lot in Ranji-Trophy cricket, and it pays off. This makes Bumrah our best bowler of the match. This (win) will give us more confidence and we will play more positively in Sydney.
"I think they've just chose to take the weather out of consideration", Harsha Bhogle told Fox Cricket as Pujara came to the crease after the fall of the first wicket, with India not appearing to be chasing quick runs.
In the Boxing Day Test though, it was India grinding it out in the first innings that actually made the difference. "The way he bowls is so much more hard and I think he realises that more than the batsmen and that's why he is so confident about his skill", said the India skipper, who is considered to be one of the best batsman in the world cricket.
"My aim is to always focus on consistency".
Mitch Marsh smacked Jadeja for a six but gave Kohli more catching practice in the covers. Stressing on the need to get Smith and Warner back in the fold as soon as possible, Paine said: "If you took Pujara and Virat out of India's side, I think you'd have the same conversation".
He asserted that irrespective of how the series is placed, the Australian batsmen are desperate to score a few more runs in order to prevent a 3-1 series scoreline.