According to the supersport.com website, India took 11.3 overs and lost both openers before Cheteshwar Pujara (eight) and Sachin Tendulkar (13) reached the target to give the hosts a lead in the four-match series.
Earlier, Australia were dismissed for 241, setting the hosts a target of 50 runs.
The visitors added nine runs to their overnight score, and it fell to part-timer, Ravindra Jadeja, to pick up the wicket of Nathan Lyon (11) to end their resistance.
Lyon withstood the attack for 77 deliveries to support Moises Henriques to the three-figure mark, but the debutant was left stranded on 81.
He faced 148 balls and hit six fours and two sixes.
Ravichandran Ashwin finished with 5-95 and Jadeda took three wickets for 72.