With the win, India closed in on achieving their best-ever series win over Australia.
Australia made 408 runs in their first innings and in reply, India took a lead of 91 runs. The winners made 499 runs in their first innings, with Murali Vijay and Shikhar Dhawan being the main contributors.
Australia top order failed to perform in their second innings and mange to give a target if just 133 runs to the opponents.
The fourth Test starts in Delhi on Friday (March 22).