Australia captain Steve Smith capitalised on India's sloppy fielding with a brilliant hundred to help set the hosts a formidable target of 441 runs to win the opening test of the four-match series on Saturday.
Australia were dismissed for 285 in their second innings to conclude an extended morning session after the visitors had resumed the third day on 143 for four.
Smith, the world's top-ranked test batsman, was out leg before to left-arm spinner Ravindra Jadeja for 109 after completing his first century in India, who will need a monumental effort to extend their 19-test unbeaten run.
The 27-year-old right-handed batsman, who was unbeaten on 59 overnight, was dropped three times on Friday and was handed another lifeline on 67 but maintained his concentration on a tricky surface to bring up his 18th test hundred.
He also enjoyed another slice of fortune on 73 when a strong appeal for leg before off Jadeja was turned down by the umpire with replays indicating the decision would have been overturned on review had India not already used up their two referrals.
After Smith reached three figures with a couple of runs off Jadeja, he punched the air and planted a kiss on his helmet before soaking up the applause from the sparse morning crowd and his team mates.
On a surface providing prodigious turn for the slow bowlers, on which India were bundled out for a paltry 105 in their first innings in response to Australia's 260, Smith was always on the lookout for runs and hit 11 boundaries in his 202-ball knock.
Smith and Mitchell Marsh added 56 for the fifth wicket before Jadeja dismissed the latter for 31 after Australia resumed with a 298-run lead.
The Australia captain had two more significant stands with Matthew Wade (20) and Mitchell Starc (30) as Australia piled on the runs.
India's off-spinning spearhead Ravichandran Ashwin added the scalp of Starc to his three wickets from Friday to finish with figures of 4-119, while Jadeja finished with 3-65.
Smith ton helps Australia set India 441 for win