Resuming the day on 108 for one in response to Australia's first innings score of 530, India lost their overnight batsmen but Kohli, registering his ninth Test century, and Rahane stitched together a record 189-run unbeaten partnership to put the visitors in a much better position.
The fourth-wicket stand is the highest partnership at the MCG by any visiting side against Australia.
Rahane, getting his third Test hundred in 13 matches, gave a simple caught and bowled chance to off-spinner Nathan Lyon (0-68) only to see it go between the bowlers palms. He was on 70.
Kohli got into a heated argument with pace spearhead Mitchell Johnson (0-82) and the verbal volleys seemed have an adverse effect on the Indian vice-captain.
He was soon dropped on 88 by Shane Watson (1-56) at first slip as a disappointed Johnson watched helplessly.
The centuries though gave the batsmen more courage to play their respective strokes as runs came thick and fast in the last half-an-hour of the session.
Kohli mixed the right dose of caution and aggression in the 171 balls that he has faced so far, his innings laced with 11 boundaries.
Earlier, Cheteshwar Pujara (25) did not trouble the scorers as the No.3 batsman was out on the second ball of the day as Ryan Harris (2-40) induced an outside edge and the catch was beautifully held by wicketkeeper Brad Haddin in front of first slip.
Opener Murali Vijay (68) did add a few runs to his overnight score and hit a couple of lovely boundaries before he got hit on the back of the helmet off a Johnson snorter.
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