At lunch, opener David Warner (58) and Shane Watson (28) were at the crease. Ashwin, who bowled 11 overs on the trot, claimed two for 30.
Electing to bat after winning the toss, the Aussies sailed along smoothly for almost 15 overs before opener Ed Cowan was stumped following a 29-run knock.
Soon after, in the 19th over, one-down batsman Phil Hughes (6) was clean-bowled by Ashwin.
On a track which Indian skipper Mahendra Singh Dhoni expected to turn from the first day itself, the hosts employed spin just 22 minutes into the match.
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Harbhajan Singh, playing in his 100th Test, and Ashwin bowled in tandem but the former was distinctly ineffective against a team, which he calls his favourite given his past record against it.
Harbhajan's 10 overs cost 42 runs and yielded no wickets for the Indians.
The pacers -- Ishant Sharma and debutant Bhuvneshwar Kumar -- shared just seven overs between them. Of the two, Bhuvneshwar seemed more impressive, managing a maiden and conceding 15 runs in his four overs even though he could not get a wicket.