India outplayed Australia by an innings and 132 runs in the first Test of the four-match series at the Vidarbha Cricket Association Stadium in Nagpur.
The team was unable to handle the spin of the Indian bowlers and was bowled out for just 91 in the second innings.
This marks the second consecutive loss for Australia in Asia, after being defeated by Sri Lanka in July.
The Indian spinners, Ashwin and Jadeja, caused havoc for the Australian batsmen and sent them tumbling down to their lowest score ever in India.
Ashwin got rid of both openers, David Warner and Usman Khawaja, and Jadeja removed Marnus Labuschagne, effectively ending any chances of Australia avoiding an innings defeat.
Alex Carey, one of the few batsmen to reach double digits, tried to sweep his way out of trouble but was caught by Ashwin for 10.
Ashwin finished with 5 wickets and Jadeja, who took 5 wickets in the first innings and 2 in the second, was named player of the match.
Australia was trailing by 223 runs at the start of their second innings and lasted only 32.3 overs before being dismissed for 91.
Steve Smith was the highest scorer with 25 runs, while only four other batsmen reached double figures.
This marks the fourth time that Australia has been defeated by an innings in India, putting a serious dent in their hopes of winning a series in the country since 2004.
The Indian team made 400 runs in their first innings, with Rohit Sharma hitting a magnificent 120, and all-rounders Axar Patel and Ravindra Jadeja proving that the pitch, although difficult, was still playable.
Even the number 10 batter, Mohammed Shami, contributed with 37 runs, leading India to a lead of 223.
Todd Murphy, a bright spot for the Australian team, took 7 wickets on his debut, but there was little else to celebrate.
The Australian wickets fell quickly in their second innings, with Usman Khawaja, David Warner, Matt Renshaw, Peter Handscomb, and Alex Carey all falling to Ashwin.
Marnus Labuschagne was caught by Jadeja, and Patel took the wicket of Murphy. Shami finished off the tail by dismissing Nathan Lyon and Scott Boland.
Australia now moves on to Delhi for the second Test match, which starts on Friday.
Players such as Cameron Green, Mitch Starc, and Josh Hazlewood hope to be fit for selection, while the non-selection of Travis Head will likely be heavily scrutinized.
After the match, Indian spinner Jadeja, who was named player of the match for his 7 wickets and 70 runs, was fined 25% of his match fee and received one demerit point on his disciplinary record.
He was found to have breached the ICC Code of Conduct and accepted the punishment from the match referee, Andy Pycroft.
India XI: Rohit Sharma (c), KL Rahul, Cheteshwar Pujara, Virat Kohli, Suryakumar Yadav, Srikar Bharat, Ravindra Jadeja, Axar Patel, Ravichandran Ashwin, Mohammed Shami, Mohammed Siraj
Australia XI: David Warner, Usman Khawaja, Marnus Labuschagne, Steve Smith, Matthew Renshaw, Peter Handscomb, Alex Carey, Pat Cummins, Todd Murphy, Nathan Lyon, Scott Boland
India 400 (Rohit 120, Axar 84, Murphy 7-124) beat Australia 177 and 91 (Smith 25*, Ashwin 5-37) by an innings and 132 runs