R Ashwin gave India the first breakthough when he dismissed David Warner on the third day of the fourth and final Test at the Adelaide Oval in Adelaide on Thursday.
Warner played across the line to a delivery and ended up giving a simple catch to Ashwin.
Earlier, India were bundled out for 272 runs in their first innings but with a lead of 332 runs, Australia did not enforce a follow-on.
The Indian innings ended when Virat Kohli (116) was trapped plumb in front of the wicket by Ben Hilfenhaus, who in his previous over had clean bowled Ishant Sharma.
Kohli’s hundred is the first century by an Indian batsman in this series.