India conceded a 97-run lead and then Australia reached 38 for one six overs to take the over-all lead to 135 runs at the tea break.
At the break, Chris Rogers (21) and Shane Watson (13) were at the crease, the latter lucky to be there as Wriddhiman Saha missed a run-out chance in the fourth over.
Earlier, in the post-lunch session, Ashwin (50) and Kumar (30) playing aggressively, especially the latter as he moved from 3 at the break to quickly score 27 more runs as the 50-partnership for the eighth wicket came about quickly.
Just as they had started eating into the lead, Kumar was given out caught at first slip off Nathan Lyon (2/123) by third umpire Steven Fry even as it appeared that the ball may have hit the ground after taking a bottom-edge.
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Mohammad Shami (16 not out) and Umesh Yadav (4) threw their bats around to reduce the deficit below 100-runs but the latter skied a catch to keeper Brad Haddin off Ryan Harris (2/96).
For Australia, Shane Watson (2/58) and Josh Hazlewood (1/64) were the other wicket-takers while Steve Smith too rolled his arm over.
India lost skipper Virat Kohli (147) in the morning session after resuming at overnight score of 342 for 5. Kohli and Wriddhiman Saha (35), who had already put on 50 runs for the sixth wicket began the proceedings and Kohli held the key for India but Australia got rid of him quickly.