Sydney: Australia recovered from the early loss of opener David Warner to be 38-1 at tea on day four of the fourth test at the Sydney Cricket Ground on Friday, leading India by 135 runs.
Ravi Ashwin struck in the second over of Australia's second innings having David Warner caught by Murali Vijay at slip for four to have the hosts at 1-6.
At the interval, Chris Rogers was 21 not out and Shane Watson was unbeaten on 13.
India missed a great opportunity to run out Watson on 8 just before tea but wicketkeeper Wriddhiman Saha fumbled the return throw by Kohli.
Earlier, Australia bowled India out for 475 to lead by 97 runs after the first innings.
Ashwin hit a half century and Kumar Bhuvneshwar made 30 as India's tail added useful runs to narrow the deficit, supplementing earlier centuries from captain Virat Kohli (147) and second-gamer Lokesh Rahul (110).
Kohli added just seven runs to his overnight score before he clipped a Ryan Harris (1-71) delivery straight to Chris Rogers at midwicket.
The new India captain belted 20 boundaries in his 230 ball knock to take his aggregate for the series to 646, bettering the previous record of 617 for the most runs by an Indian batsman in a series in Australia. Rahul Dravid had set the previous mark in 2003-04.
Saha was other batsman dismissed in the morning session, being taken on the gloves when attempting to pull at a Josh Hazlewood (1-64) short ball, and looping a catch to Steve Smith at slip.
Ashwin and Kumar added 65 for the eighth wicket — helped by a dropped chance by Joe Burns at bat-pad — before Kumar edged Nathan Lyon (2-123) to Watson at first slip for 30.
Mitchell Starc (3-106) removed Ashwin, caught by Brad Haddin for 50, before Ryan Harris (2-96) had Umesh Yadav (4) caught by Haddin to end the innings.
It is the first time both teams have surpassed 400 runs in the first innings of each test in a minimum three-test series.
The hosts have an unassailable 2-0 series lead, and regained the Border-Gavaskar trophy, with two wins and a draw in the first three tests.