Kohli was in magnificent touch as he smashed his runs from just 117 balls, hitting seven fours and two towering sixes to the delight of the huge contingent of Indian supporters at the MCG.
In the process Kohli became the fastest man to reach 7,000 ODI runs, taking 161 innings to reach the milestone, four fewer than South Africa's AB de Villiers.
The 27-year-old from Delhi came in with India at 15 for 1 after in-form opener Rohit Sharma edged Kane Richardson to wicketkeeper Matthew Wade for six.
Kohli and Shikhar Dhawan batted patiently, taking few risks and bringing up the 100 in the 22nd over.
They began to accelerate and Dhawan, who had been out of form in the first two ODIs, began to at last find the middle of the bat.
Kohli reached his 50 in the 23rd over and Dhawan the next ball with neither looking in any trouble.
But on 68 Dhawan tried to glance John Hastings and was bowled when the ball hit his pad and cannoned into the stumps.
Ajinkya Rahane joined Kohli in the middle and took up from where he left off in Brisbane on Friday, scoring a run-a-ball 50 until he tried to smash Hastings over the fence at long off and found Steve Smith, who caught the ball just inside the boundary and threw it infield to Glenn Maxwell before stepping over the rope.
Kohli eventually popped up a Hastings delivery to George Bailey at cover, but skipper Mahendra Singh Dhoni came in and smashed 23 from nine balls to get India to their final score.
Australia lead the five match series 2-0.