Ravichandran Ashwin (33) and Bhuvneshwar Kumar (3) were at the crease as India saved the Follow-on but still trail by 165 runs.
India resumed at overnight score of 342 for 5, with Kohli and Wriddhiman Saha (35), who had already put on 50 runs for the sixth wicket. Kohli held the key for India this morning and Australia got rid of him quickly.
The Indian captain had added only seven runs to his overnight score when, in the fifth over of the morning, he clipped Ryan Harris (1/71) to mid-wicket only for Chris Rogers to take a low catch.
Ashwin walked out to the middle and batted with solidity as he and Saha put on 31 runs for the seventh wicket. They made sure that Australia will have to bat again to force a result.
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Saha batted extremely well, showing a good temperament in his short but very useful innings. He was undone by Josh Hazlewood (1/58), a short delivery taking his glove on its way to Steve Smith in the slips, who didn't make any mistake this time around after two drops on day three.
However he was lucky to be still at the crease as Joe Burns failed to latch on to a lobbed up ball off his bat-pad off Nathan Lyon (1/102). He had not opened his account at that time. But he avoided any further hairy moments and helped India cross the 400-mark as the tail started eating away into Australia's lead.
For the hosts, Mitchell Starc (2/101) and Shane Watson (2/51) are the other wicket-takers.