Brief scores: India 303/4 (Pujara 130*, Agarwal 77, Vihari 39*; Hazlewood 2-51) vs Australia.
The landmark was his 18th century in his 68th Test and follows a stellar 123 in the first Test in Adelaide and 106 in the third Test at Melbourne.
Hanuma Vihari ended 39 not out with India, who lead 2-1, needing a draw to clinch a first series win in Australia. Rahul edged through slips for 4 in the first over and was unable to hit the middle of the bat before Hazlewood got the edge to Shaun Marsh at first slip.
Kohli's team has conquered Australian conditions with aplomb this summer but pitches have been a near-constant talking point throughout the series, with the Perth and Melbourne decks both rated average by the match referee.
He survived a review decision for caught behind on 12 but was otherwise unmovable.
North Korean diplomat in Italy 'seeking asylum'
USA officials have said the extent of initial North Korean steps was not confirmed and could be easily reversed. The source could not confirm the newspaper report or whether Mr Jo was still based in Italy.
Chang'e-4: China space mission lands on far side of moon
While the far side of the Moon has been photographed since the 1950s, humankind has yet to successfully land there until now. Next year, Chang'e 5 should bring samples back from the moon, also a first since 1976, according to the Associated Press.
Airline to honor $16,000 first-class fares it accidentally sold for $675
The pricing mistake was first noticed several days ago by aviation bloggers, who trawl the internet looking for cheap deals. Airlines often honour tickets sold in error, but practices differ from carrier to carrier and according to circumstances.
Agarwal continued his impressive introduction to test cricket with another half century.
He worked hard to make his second Test 50 in only three innings by caressing a Mitchell Starc delivery through the covers for four.
With India winning their first Boxing Day Test, Kohli equalled predecessor Sourav Ganguly to win the most number of Tests overseas and also became only the second Indian captain after Bishan Singh Bedi to win two Tests Down Under.
Master batsman Kohli was welcomed by boos from a section of the crowd and immediately silenced them with an exquisite four off Hazlewood.
Australia produced the breakthrough soon after Tea, when Kohli was strangled down the leg side by a short ball from Josh Hazlewood. On Tuesday, as the Indian and Australian teams reached the official residence of Australian Prime Minister Scott Morrison in Sydney on the occasion of the New Year's Day, Kohli was introduced as a "cricket crush".
Australia made two changes, with Aaron Finch and Mitch Marsh left out and Labuschagne and Peter Handscomb included, while India brought in Rahul and Kuldeep Yadav for Rohit Sharma and Ishant Sharma.