Cheteshwar Pujara batted throughout the day to reach his 11th Test century as India battled for parity on the third day of the third Test in Ranchi.
Pat Cummins provided a constant threat for Australia, finishing with four for 59, but could not breach the defence of Pujara, who ended unbeaten on 130 as India reached 360 for six at the close, still 91 runs behind the tourists' total of 451.
Murali Vijay (82) helped put on a partnership of 102 for the second wicket with Pujara before some hostile bowling from Cummins, in his first Test for six years, dragged Australia back into the contest.
Starting the day on 120 for one, the home side made comfortable progress through the morning session, but were fortunate not to lose two quick wickets shortly after the drinks break.
Pujara was the beneficiary of a marginal lbw call, prompting Australia to review unsuccessfully as Steven O'Keefe looked to have beaten the inside edge of the bat, only for replays to prove inconclusive before the original decision was upheld.
That was Australia's second unsuccessful review of the innings, and they were made to rue their wastefulness with the very next delivery as Vijay edged the ball onto his pad and was caught at short-leg off Nathan Lyon, only for the umpire to wave the appeals away.
O'Keefe finally made the breakthrough the ball before the lunch break, tempting Vijay to wander down the pitch before missing a straight ball to allow Matthew Wade to smartly whip off the bails.
Kohli's miserable series continued as he drove loosely at Cummins shortly after the new ball was taken, edging to Steve Smith at second slip for six to give the tourists some momentum and leaving the Indian skipper with just 46 runs in the series.
Ajinkya Rahane made 14 before becoming Cummins' third victim, before Josh Hazlewood jagged one back to bowl Karun Nair for 23 as Pujara battled on at the other end, reaching three figures from 214 balls in a trademark gritty knock.
Cummins produced a rip-snorter to have Ravi Ashwin caught behind as Australia tightened the screw in a final session, but Saha and Pujara saw India through to stumps with the match evenly poised.