Kohli, standing in for injured regular captain Mahendra Singh Dhoni, became the first Indian after Vijay Hazare and Sunil Gavaskar to score a hundred on his debut as skipper of the team.
The 26-year-old's seventh ton in the five-day format ended at 115 after he was dismissed by Mitchell Johnson off a short-pitched delivery just before stumps. The Indian's attempted pull landed in the hands of Ryan Harris at deep fine leg in the 95th over of the day.
The resolute effort by the Indians, undone to an extent by Kohli's late dismissal, came after the Australians declared their first innings at an overnight score of 517/7.
On a bright and sunny day which started early to make up for the four hours of play lost yesterday due to rain, the Indians dominated the proceedings for most part before Kohli's wicket swung the equations slightly in Australia's favour.
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Earlier in the morning, opener Shikhar Dhawan (25) departed in the eighth over but the rest of the top-order fired in unison to put India in a comfortable position on a placid track.
In between, Ajinkya Rahane (62) also managed to clinch his fifth Test fifty as Australian bowlers toiled just the way their Indian counterparts had to on the first two days of the match.
Pacer Mitchell Johnson bent his back to send down a couple of probing spells but the wickets were hard to come by. Johnson, the most menacing of all the Aussie pacers today, ended the day with figures of 2/90 in his 18 overs -- Kohli's wicket being his most crucial strike.