Now that the series can't be lost, India can breathe a little easy, but Bumrah's partners in Sydney - a Test, Kohli said, India want to win and not just hang on to for a draw - will be crucial.
Rishabh Pant's dismissal of Tim Paine equalled him with Syed Kirmani and Naren Tamane for the record of most dismissals by an Indian in a Test series.
India has taken a 2-1 series lead with a 137-run win over Australia on day five of the Boxing Day Test, securing the Border-Gavaskar trophy.
They were chasing an unlikely target of 399 but were helped when rain began to fall in Victoria on Sunday morning.
No team before had made more than 332 to win, and that was in 1928 by England.
Following India's innings, there were a lot of talks regarding the pitch and how India's "slow batting" had cost them the Test match.
"We always believed that this was very possible because of the talent we have in the side and the mindset we have been carrying for the last 12 months", Kohli said. That'd be a pretty good result against the No.1 team in the world.
Tailender Cummins, who is rapidly proving himself to a very capable all-rounder, tipped by some as a future Australia captain, had kept his side in the hunt with an impressive 61 not out on Saturday. Lyon added one to his overnight total.
Khawaja and Marsh both unsuccessfully reviewed their marching orders, with the ball-tracking replay nearly saving the latter and denying Bumrah his eighth wicket of the match.
Bumrah, who picked three wickets in Australia's second dig to add to his tally of six in the first innings, now has 48 Test scalps in just nine matches.
India have made a habit of preparing pitches heavily suited to their spinners, although it backfired previous year when Australia claimed a surprise Test victory in Pune on a dustbowl surface that Shane Warne likened to "the surface of Mars".
Earlier, Cummins had taken a career-best 6-27 when India declared their second innings on 106-8 before lunch.
India, denied victory on day four by the tail-end resistance of Pat Cummins, was forced to wait almost two-and-a-half hours for play to begin due to rain at the Melbourne Cricket Ground but when the weather cleared their bowlers wrapped up Australia's innings for 261 in 22 minutes.
Three Tests gone, one to go.
"And now we have the bowling attack that we can rely on to get us 20 wickets and his role becomes even more crucial".
When Shaun Marsh was also trapped leg before by Bumrah for a brisk 44 and his brother Mitch - another candidate for the Sydney chop - fell for 10, Australia's faint survival hopes were fading fast.