A big century from skipper Steve Smith led Australia to a formidable first innings total of 451 before India's openers survived a probing pace attack on day two of the third Test Friday.
The hosts were 20 for no loss at tea in Ranchi, with Lokesh Rahul (18) and Murali Vijay (two) batting at the break. India still trail the visitors by 431 in their first innings.
Smith's unbeaten 178 was the bedrock of the tourists' innings which also featured a maiden Test century by allrounder Glenn Maxwell.
After resuming in the morning on 299-4, Smith and Maxwell put on a 191-run partnership to help the tourists post the biggest innings total so far in the four-match series.
Left-arm spinner Ravindra Jadeja claimed his eighth five-wicket haul in his 29th match to return with figures of 5-124.
Jadeja ran out last man Josh Hazlewood (0) to deny Smith the chance of posting the second double century of his career.
Earlier the 28-year-old Maxwell set the tone for Australia's continued dominance with his maiden Test century in just his fourth Test since making his debut in 2013.
India's plight was deepened by the absence of skipper Virat Kohli who has been off the field since Thursday afternoon with an injured shoulder.
While vice-captain Ajinkya Rahane stood in for Kohli, the star batsman is expected to don the pads in what remains a crucial Test for the hosts.
The four-match series between the world's top two sides is tantalisingly poised at 1-1 with India needing at least a draw to have any chance of winning back the Border-Gavaskar Trophy.