The Aussies are ahead of India by just two runs and have four wickets in hand. India are yet to bat in the second innings.
The Time Paine-led side, which had dismissed India for 326 and restricted the lead to 131 runs early on the third day, however, found the going tough in the second innings as it kept losing wickets at regular intervals.
The Aussies eventually found themselves at 99 for the loss of six wickets at one point and in danger of losing the game by an innings.
However, all-rounder Cameron Green and bowler Pat Cummins saw off the last 18 overs without any further casualty, adding 34 in the process.
Pace bowler Umesh Yadav removed Joe Burns early before limping off the field following pain in the ankle. He has undergone scans and did not take field after limping off in his fourth over.
Marnus Labuschagne was dismissed with the Aussie team total on 42, removed by off-spinner R Ashwin. Then Steve Smith was bowled down the leg, by a Jasprit Bumrah delivery. The Aussie batting mainstay had left his leg-stump exposed. A flurry of wickets followed with opener Matthew Wade, who had batted well for his 40, Travis Head and skipper Tim Paine getting dismissed within one run.
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The Indian bowlers shared the wickets with Jadeja taking two and the others -- Bumrah, Umesh, Mohammed Siraj and Ashwin, taking one each.
Earlier, India were all out for 326 in first innings. Both skipper Ajinkya Rahane and Ravindra Jadeja looked good on resumption. However, the run out of Rahane (112) led to a flurry of wickets. India lost the last five wickets for just 32 runs. Jadeja though managed to complete his half-century (57).
Brief scores: Australia 195 and 133/6 (M Wade 40, M Labuschagne 28, R Jadeja 2/25) vs India 326 (A Rahane 112, R Jadeja 57, S Gill 45, M Starc 3/78, P Cummins 2/80, N Lyon 3/72).