While captain Mahendra Singh Dhoni expectedly got the man-of-the-match award for his game-changing knock of 224, off spinner Ravichandran Ashwin scalped 12 wickets in the match to also play a stellar role.
The margin of victory could have been bigger had the Indians managed to get rid of the last wicket pair yesterday itself and had they not lost both their openers despite chasing a small total.
The two teams will now travel to Hyderabad for the second Test be played at the Rajiv Gandhi International stadium from March 2 to 6. This was the third time that Indian spinners managed to take all the 20 wickets in a match.
The first time that Indian spinners bagged all the 20 wickets was at this same venue against England in 1972-73 while the second such instance was against New Zealand in Auckland in 1975-76.
Resuming at the overnight score of 232 for nine, Australia could add just nine runs to their tally much to the relief of the Indians who had a frustrating time trying to
dismiss the last-wicket pair.
It took the Indians just nine overs this morning to put an end to Australia's resistance when Ravindra Jadeja broke the agonisingly long last-wicket partnership between Henriques and Lyon.
Lyon, who showed a lot of grit and temperament to hang on, was dismissed by left-arm spinner Jadeja, caught by Murali Vijay at short-leg.
Henriques followed up his first innings half century with another gutsy unbeaten 81 and together with Lyon added 66 runs for the final wicket to take the match into the fifth and final day and prevent India from recording an innings victory.
Chasing the paltry 50-run target, India suffered two early blows in the form of openers Sehwag and Vijay, whose flop show with the bat continued.
The opening duo of Sehwag and Vijay put on 16 runs before the former was the first one to depart.
Vijay started his innings with a bang, smacking Lyon straight over his head for a six, his only scoring shot of the innings.
But that was all the local boy could manage in the innings as he was caught by Henriques at mid-off off James Pattinson when he tried to go a big drive in the next over.
India clinched the first cricket Test against Australia with a comfortable eight-wicket victory to take a 1-0 lead in the four-match series in Chennai on Tuesday with their spinners