Ravichandran Ashwin tore through Australia in their second innings to set up a comprehensive victory for India by an innings and 132 runs inside three days of the spin-dominated opening test on Saturday.

Australia had been on the back foot since posting a below-par 177 on a treacherous track, and India's victory appeared just a matter of time after the home side amassed 400 to claim a hefty lead of 223.

Ashwin (5-37) then hollowed out Australia's top order with his nagging accuracy, and the tourists were skittled out for 91, losing all 10 wickets in one frenetic session.

Steve Smith's unbeaten 25 was the highest individual score in Australia's sorry-looking second innings scoreboard, which is likely to prompt some soul-searching heading into the second test in New Delhi from Friday.

Off-spinner Todd Murphy claimed 7-124 in his debut test in what was the only highlight for world number one Australia, who still lead World Test Championship standings ahead of India.

Rohit Sharma's majestic 120 had put India in the box seat and all-rounders Axar Patel (84) and Ravindra Jadeja (70) drove home the advantage on day three of the contest.

Mohammed Shami (37) chipped in with a breezy cameo down the order before India folded for 400 on the stroke of lunch.