The hosts, looking to complete a series whitewash, were frustrated early on by tail-enders Peter Siddle and James Pattinson, who had joined forces on day one with the tourists 189 for eight and continued their stubborn resistance on the second morning.
Siddle, resuming on 47, reached his maiden Test fifty before being bowled between bat and pad for 51 to hand R Ashwin his five-for.
Pattinson (30) was the final wicket to fall, left-arm spinner Pragyan Ojha snaring his 100th Test wicket - in only his 22nd Test - by inducing a leading edge which was snapped up by Virat Kohli at slip.
India's reply got off to a solid start, openers Murali Vijay and Cheteshwar Pujara offering few chances to Australia's pace attack of Mitchell Johnson, Pattinson and Siddle. The pair were unbeaten on 23 and 28, respectively, after the first session.