Australia had earlier declared their second innings at the overnight score of 251 for six, which gave them an overall lead of 348 runs.
India still need 276 more runs to win with two full sessions of play remaining.
At the break, Murali Vijay was batting on 35 off 77 balls with the help of two fours and one six, while giving him company was Rohit Sharma on 13 off 57 balls, during which he struck one boundary and a six. The duo had put on unbeaten 25 runs for the second wicket after the loss of Lokesh Rahul (16)
The day started with Australia skipper Smith declaring at the overnight score and giving India 90 overs for their first win in this series.
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Vijay and Rahul then walked out to the crease, full of purpose, but they started slowly. They were both watchful against the new ball and hence the runs came in a trickle. Only nine runs came in the first seven overs, with Lyon being introduced into the attack as early as in the sixth over.
But while he was looking good at the crease, Rahul was struggling and after adding 48 runs for the opening wicket with Vijay, he ended up gloving one off Lyon in the 14th over to David Warner at backward short leg.
Rahul's dismissal brought Rohit to the crease and he could have been out first ball, but survived a huge stumping chance by the narrowest of margins.
Thereafter, he took his time to settle down as there were no runs scored for 6.4 overs after the fall of Rahul. The 50-run mark came up when the Indians finally broke through the silence in the 20th over. Rohit then lashed out against Lyon hitting him for a four and a six in the 24th over, moving the scoreboard along to catch up for the lost time.