Khawaja then led the tourists to 156-4 in reply, with Peter Handscomb seven not out at the close of play and Cameron Green unbeaten on six.
Earlier, India lost seven wickets in a hectic morning session.
Rohit Sharma appeared to be out twice in the first over, caught behind and lbw, but umpire Nitin Menon was unmoved while Australia opted not to review on both occasions.
Kuhnemann finally had Sharma stumped for 12 before Shubman Gill was caught at slip for 21.
Nathan Lyon (3-35) then bowled Cheteshwar Pujara for one as the ball started turning sharply, and Ravindra Jadeja was caught at cover for four.
India slumped to 45-5 when Shreyas Iyer was bowled for a duck, going for an expansive cut.
Virat Kohli batted with caution to score 22 off 52 balls but he eventually fell to spinner Todd Murphy.
Srikar Bharat was then lbw to Lyon for 17 as India reached lunch on 84-7. Things got no better for the hosts after the interval as Ravichandran Ashwin was caught behind for three off Kuhnemann.
Kuhnemann added his fifth wicket when he trapped Umesh Yadav lbw for 17, and the innings ended when Mohammed Siraj was run out for a duck.
Australia then lost an early wicket when spinner Jadeja trapped Travis Head lbw for nine.
Jadeja also bowled Marnus Labuschagne off a no-ball before the Australian number three escaped a good lbw shout from Ashwin.
Labuschagne went on to share a stand of 96 with Khawaja, who was the pick of the batsmen on both sides, before falling to Jadeja for 31.
Jadeja also ended Khawaja’s stay when he had the opening batsman caught at deep mid-wicket. The Indian spinner ended with 4-63 after also having Steve Smith caught behind for 26.
Khawaja said: “It is a very spin friendly wicket out there. It was tough to play and it won’t get any better. I had a challenging time throughout.”
India has an unassailable 2-0 lead in the four-match series. It needs another win in the remaining two games to qualify for the world test championship final on June 7.
- AP
