Murali Vijay's scoreless early dismissal left India at six for one at lunch after Australia's first innings folded for 326 on the second day of the second Test, here Saturday.
Australia's lower order added crucial 49 runs after resuming at 277 for six as paceman Ishant Sharma finished with 4 for 41.
Mitchell Starc (1/2) bowled Murali Vijay for a 12-ball duck to give Australia bragging rights from the morning session as India trail by 320 runs on a tricky wicket.
Skipper Tim Paine (38) and Pat Cummins (19) frustrated Indian bowling and extended their eighth-wicket partnership to 59 runs.
In doing so, they took Australia past 300 in the 100th over. For their part, India were guilty of bowling too short again and there weren't enough full deliveries attacking the stumps or making batsmen play.
India were content with keeping a lid on the scoring as only 29 runs came in the first hour of play. They started the day's proceedings with Ishant and Mohammed Shami (0/80), with Umesh Yadav (2/78) starting as first change.
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Jasprit Bumrah (2/53), who was India's standout bowler on day one, was the fourth to bowl in an inexplicable tactic from the skipper.
There was certain hint of variable bounce from the pitch, but again India didn't bowl full enough to exploit the same as the Australian tail wagged.
Finally, Yadav got the breakthrough with an over of full deliveries, knocking off Cummin's off-stump in the 105th over. Two balls later, Bumrah trapped Paine lbw and the decision stayed despite a DRS review from the batsman.
Nathan Lyon (9 not out) stayed unbeaten for the third innings in a row as he added quick-fire 16 runs with Mitchell Starc to push Australia to a healthy total on a tough wicket.
Ishant then finished off things with two wickets in two balls, with Starc and Josh Hazlewood (0) caught behind with some acrobatic help from Rishabh Pant.
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