Ashwin grabbed five for 63 while Ravindra Jadeja took three for 33 as Australia displayed surprising lack of fighting spirit to be skittled out for a meagre 131 in 67 overs in their second innings.
The match lasted only two hours on the fourth day as it was an abject surrender by the Australian batsmen who had no answer to the questions posed by Ashwin and Jadeja on a turning track at the Rajiv Gandhi International stadium.
The visitors needed 192 runs to avoid an innings defeat but they lost the final eight wickets in 35 overs with an addition of only 57 runs to their overnight total.
When Ashwin dismissed Pattinson to get the final wickets, the 10,000-odd spectators erupted in joy but the celebration from the Indian camp was a muted one as they only engaged in handshakes.
Cheteshwar Pujara was deservingly awarded the man-of-the-match award for his double hundred. Read more: Doubled over after another double
The teams now have an eight-day break before the third Test in Mohali but the way this series has panned out, there is unlikely to be any change of script in the third Test where the hosts would be aiming to wrap up the series. Read more: Some praise must be reserved for flat tracks
It's a well-documented fact that Australians can't play spin bowling which was endorsed by Pujara but what was sad to see was their inability to even put up a fight. Read more: Aussies don't know how to go about on turners: Pujara
Such was the domination of the Indian spinners that Australia lost their last three wickets for an addition of only one run in 10 overs.
The last Test played in Hyderabad against New Zealand also ended inside four days but it was more to do with majority of the second day's play being washed out.
With this win, Mahendra Singh Dhoni has become the most successful Indian captain, eclipsing Sourav Ganguly's record of 21 Test wins.