Steve Smith on Saturday cracked his maiden century in India to help Australia set the hosts a daunting 441 to win the first Test in Pune.
The visitors, who resumed day three on 143-4, were bowled out for 285 in an extended morning session which ended with the wicket of Steve O'Keefe (6) and lunch was called.
Skipper Smith dominated play to take his overnight score of 59 to 109 as he tackled India's bowlers with aplomb till he fell to left-arm spinner Ravindra Jadeja.
Indian off-spinner Ravichandran Ashwin claimed four wickets while Jadeja took three.
Smith, who survived three dropped catches on Friday, lived dangerously after surviving another spilled chance on 67 and a close lbw appeal on 73.
The world's top batsman went on to register his first ton on Indian soil and the 18th of his career, jumping with joy and kissing his helmet after reaching the three-figure mark.
India were at the receiving end of some dodgy decisions including Smith's lbw and a caught behind of Mathew Wade but had already utilised their two reviews on day two.
Wade though couldn't capitalise on his luck, falling to Umesh Yadav a couple of balls later.
Smith, who struck his fifth consecutive ton against India since the 2014-15 series in Australia, was finally trapped lbw off Jadeja and taking a review proved futile.
Mitchell Starc, who scored a gritty 61 in Australia's first innings score of 260, hit a breezy 30 with 2 fours and 3 sixes.
But it was left-arm spinner Steve O'Keefe who put Australia in a commanding position after his career-best haul of 6-35 helped skittle out India for 105 on Friday. The hosts conceded a crucial 155-run lead.
Number-two ranked Australia, who lost their last nine Tests in Asia, are looking for an upset win against the world's top side.