Resuming the day on 108 for one in response to the hosts' first innings score of 530, India lost their overnight batsmen early but Kohli (169), registering his third ton in this series, and Rahane (147) made sure that their stand is the highest for India in Australia at the MCG for any wicket.
The visitors ended the day on 462 for eight as they still trail by 68 runs at the end of Day 3. Aided by five dropped catches, India responded well only to lose a bit of a momentum in the end as new-ball bowler Ryan Harris returned with figures of 4-69.
Pace spearhead Mitchell Johnson (1-133), who bled runs through the day, also got Kohli caught behind to get a consolation wicket as umpires called stumps.
Getting into heated exchanges with Johnson at different stages of his innings, Kohli was dropped on 88 by Shane Watson (1-65) at first slip in the 85th over and made full use of the spill. Kohli, recording his ninth Test ton, mixed the right dose of caution and aggression in his 272-ball stay, his innings laced with 18 boundaries.
(Also read: Virat slams ton, blows a kiss to Anushka! )
Rahane, who got his century in just 127 balls, hitting 21 fours in his three-hours ten minute stay in the middle. Rahane was finally trapped lbw off Lyon but not after maintaining a strike rate of 85.96.
Rahane's wicket opened up the gates for the host, who struck back with four wickets for 53 runs in the final session of play. Debutant Lokesh Rahul (3) failed to capitalise on a dropped chance at mid-wicket off Lyon only to play another similar stroke against the off-spinner on the very next delivery as the ball took a top adge and settled into the hands of Josh Hazlewood (0-75) at fine leg.
Skipper Mahendra Singh Dhoni (11) fiddled around for sometime but his tentative approach from the very start cost him his wicket after Harris got the wicketkeeper-batsman caught behind.
Ravichandran Ashwin was the next as part of the mini-procession and the No.8 batsman could only face four balls before being caught and bowled off Harris for a nought.
Also read: HIGHLIGHTS: India-Australia third Test (Day 3)