Resuming the day at 74 for two, Australia suffered yet another batting collapse and were skittled out for 131 in the second innings by lunch on the fourth day.
Australia, who had declared their first innings at 237/9, earned the dubious distinction of becoming the first team in the history of Test cricket to lose by an innings after declaring their first innings.
India, despite suffering a massive batting collapse on the third day, got to 503 in the first innings, courtesy a 370-run stand between Cheteshwar Pujara (204) and Murali Vijay (167). Pujara, for whom it was his second double ton, was adjudged as Man of the Match.
With the win, skipper Mahendra Singh Dhoni surpassed Sourav Ganguly as the most successful Indian Test captain.
Going into day four, India were in firm control of the match as they were just eight wickets shy of an innings win. For Australia, it was always going to be a herculean task to make India bat again.
The Australian batting crumbled like a pack of cards against the spin duo Ravichandran Ashwin (5/63) and Ravindra Jadeja (3/33).
Pacer Ishant Sharma was the first to strike to remove Shane Watson (9) for his first wicket of the series. Watson tried to play a length ball down the leg-side but played too fine and Dhoni took a nice diving catch.
Left-arm spinner Jadeja struck in his consecutive overs to get rid of skipper Michael Clarke (16) and Ed Cowan (44) as Australia slumped to 111/5.
For the second time in the match, Jadeja rattled Clarke's stumps and then removed overnight batsman Cowan as Sehwag took a good catch at first slip after the ball ricocheted off Dhoni's pads.
Jadeja also put on a fine show on the field with a direct throw from the cover to get rid of Moises Henriques, who didn't trouble the scorers, with the score stranded at 111/6.
The last four wickets fell for just 20 runs as Ashwin and Jadeja attacked in tandem to wrap up the tail.
Both the teams now travel to Mohali for the third Test from March 14. The fourth and the final Test will be played in Delhi from March 22.