Having taken the last three Australia wickets to bowl out their hosts for 235, India reached 151-3 - off 61 overs - for a second-innings lead of 166.
"A 4-0 series win for Australia will move them into No.1 position in Test rankings; India need to draw one Test to retain top spot", the ICC said in a statement.
Travis Head, who scored 72 to nearly drag Australia to first-innings parity, described the match as evenly poised and backed his side to chase down anything.
"It's slightly in our favour. we'll have a good lead if we capitalise tomorrow", paceman Jasprit Bumrah said.
"They are pretty poor shots, really, from top-order global players", Ricky Ponting said in commentary for the Seven Network.
After a day of toil, Nathan Lyon took his first wicket of the innings when he snared the Indian captain for 34 with 15 minutes to go, thanks to a bat-pad catch by Aaron Finch.
The highest successful run chase in a Test at the venue is Australia's 6-315, achieved in 1902 against England, while no side has chased down more than 236 since West Indies in 1982.
Their in-form No. 3 batsman Usman Khawaja stuck around for 125 balls scoring 28 runs before falling to in-fire Indian spinner Ravi Ashwin, who finished the day with three scalps.
The second decision overturned courtesy Pujara's appeal for a review had the same protagonists as the first DRS - the bowler was Lyon and the umpire was Llong.
"You love seeing that passion in sport. Mind you, I think if we did that at the moment, we'd be the worst blokes in the world", Australian coach Justin Langer told Fox Cricket before the start of play.
Kohli, given a heated reception by some sections of the 30,348-strong crowd, ditched the histrionics when he walked out to bat with India 76-2 and the game in the balance.
Many applauded the move but the true merit of it will be known until after a four-man Australian attack has ploughed through a predicted furnace over the next few days where on-field temperatures are expected to soar into the late 30s. Thereafter, the likes of KL Rahul and Murali Vijay cobbled together a stand of 63, which laid the platform for the visiting team to build on their lead.