At lunch, India were 415/7 with Ravichandran Ashwin and debutant Jayant Yadav batting on 47 and 26, respectively.
Batting on 151 overnight, Kohli got out for 167 at the Dr. YS Rajasekhara Reddy ACA-VDCA Cricket Stadium, missing out on what would have been a rare feat by 33 runs.
On a wicket that started turning, Ashwin and Yadav showed fine application.
But Ashwin, who was dropped on 17, played beautifully and added an undefeated 52-run partnership with Jayant. With Ali looking to bowl the hosts out, the duo held on as they looked set for a big total after resuming the day on 317/4.
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With the second new ball only two overs old, England started with their two frontline pacers in Anderson and Stuart Broad, but there was little assistance for them from the pitch.
Kohli and Ashwin went about their tasks and it was the introduction of spin, in Ali, that provided the breakthrough in the 11th over.
Eyeing a third double century in a calendar year, Kohli looked in no trouble against the duo of Anderson and Broad.
(REOPENS DEL05)
Having got the solitary breakthrough of Lokesh Rahul yesterday, Cummins was brought in the ninth over of the day by Australian captain Steve Smith. Cummins bowled three successive maiden overs conceding eight runs from his nine overs before he was replaced by Nathan Lyon as Australia resorted to spin from both ends.
There were some anxious moments for the Indians when Pujara, on 22, survived while trying to play a forward defence off O'Keefe only to be trapped in front. The subsequent appeal was turned down by umpire Chris Gaffaney as Australia went for their second and last remaining review.
Luckily for Pujara, he had some inside edge though replays did not confirm whether it was bat or pad first, and he survived. The Australians ran out of the two reviews permitted in 80 overs.
Australia had their first unsuccessful review in the 39th over when their call for bat-pad against Vijay was turned down yesterday.