India set a target of 162, but despite losing three wickets in pursuit, Australia managed to reach 162/4, with Travis Head unbeaten on 34 and Beau Webster not out on 39.
“It's one thing to have a plan, but then to be able to execute that, the way that we have to Virat, (to) put him under immense pressure," said Australia men’s coach Andrew McDonald.
The acclaimed 37-year-old opener Rohit has had a poor series and the writing was on the wall when he failed to show up for India's pre-match press conference.
Walking out at 17/2, Kohli edged a delivery from Scott Boland towards Steve Smith at second slip, with Smith reaching low to his right. With the red Kookaburra wedged between his thumb and index finger, Smith went on to scoop the ball in the direction of Marnus Labuschagne - who caught the ball - before Kohli stood his ground.
Kohli had a huge left-off on his first ball and finally departed for 17, following KL Rahul (4), Yashasvi Jaiswal (10) and Shubman Gill (20) who were out before lunch.
Regular skipper and opener Rohit was "rested" for Sydney Test, India said, after failing to get past 10 runs in any of his five innings during the series, which Australia lead 2-1.
His comments follow the blockbuster fourth Test between India and Australia that drew a record 373,691 spectators to the Melbourne Cricket Ground over five enthralling days.
Opener Rohit has just one fifty and 10 single-digit scores in his last 15 Test innings, and even a move down the order failed to pay dividends for the 37-year-old.
A draw in Sydney would be enough for Australia to reclaim the Border-Gavaskar Trophy contested between the nations, which India, winners of the last four series, have long held.
"He's the MVP, isn't he? Most valuable primate," she said on Sunday while commentating for Fox during the second day's play at the Gabba in Brisbane.
Needing 245 to avoid the follow-on, India lost wicketkeeper Rishabh Pant during a stop-start session in which only 6.5 overs were bowled because of three rain delays.
Despite Jasprit Bumrah’s 12th five-wicket haul in Tests for the visitors, the hosts had a field day with the bat.
While the ton was his first in 24 Test innings - the previous having come against England in the Ashes last year - Smith believes he was ticking all the boxes over the past month in the lead up to the series.
Head scored a magnificent 152 and Smith a gritty 101 at the Gabba in Brisbane to put Australia into a strong position to go 2-1 up in the five-Test series.
In the wake of India's 10-wicket thrashing inside three days in the second Test at Adelaide on Sunday, there will be a growing clamour for Shami to be parachuted into Brisbane for the third test against the hosts.
The pink-ball Test in Adelaide between Australia and India saw tempers flare during a high-stakes five-match series with significant World Test Championship implications.
After being thumped by 295 runs in Perth, the hosts responded emphatically at Adelaide to wipe out Rohit Sharma's men inside three days and leave the five-match series evenly poised at 1-1.
The hosts won the day-nighter in Adelaide by 10 wickets to level the series 1-1 and with less than a week before they meet again at the Gabba, India are racing against the clock to fix what went wrong.
Smarting from their comprehensive defeat in the opening Test in Perth, Australia bounced back in style at Adelaide Oval, where they now have a perfect 8-0 record in pink ball tests following the 10-wicket win over India.
