India made light work of their second innings chase as they reached the 77 required with nine wickets in hand, with Cheteshwar Pujara unbeaten on 41 after just 15.3 overs.
India thus hold a 1-0 series lead as they head to the second Test in Mumbai, where England will have a lot to think about in terms of their fast bowling, as well as their under-performing batting line-up.
England lost five wickets in the morning session for just 66 runs to be all out for 406 at lunch, leaving India a meagre total to chase. The only man out for India was Virender Sehwag, who was wonderfully caught on the boundary by Kevin Pietersen off Graeme Swann.
England started the day on 340 for five, with Alastair Cook on 168 and Matt Prior on 84. The duo looked comfortable early on, but for some reason they both played shots to get out that made it seem like they'd just arrived in the middle.
Prior was caught and bowled by Pragyan Ojha for 91, tamely popping a looping delivery straight to the spinner. Cook fell 10 runs later on 176, caught in no-man's-land and bowled through the gate, also to Ojha. They had put on 157 runs together.
This left Tim Bresnan and Stuart Broad to try and push the score up while staying in the middle, but Broad could only add three before catching a leading edge off Umesh Yadav, who took the catch on his follow through.
Swann then came in and tried to play all manner of shots ala Kevin Pietersen, employing the switch hit a number of times, to varying degrees of success. He'd struck two fours and a six in his 17 runs, before Ravi Ashwin got the last laugh and removed his middle stump as he tried to play another switch shot.
Bresnan was the last man to fall, caught by sub fielder Ajinkya Rahane off Zaheer Khan's bowling, bringing on the lunch break and India's impending victory.
India went all guns blazing from the get-go, with Pujara looking in sublime touch after his double ton in the first innings. He and Sehwag went at nearly seven to the over before the latter's dismissal, and then Virat Kohli can in to wrap up the match.
The second Test starts on 23 November in Mumbai, where England will be without Ian Bell as he has flown home to be with his wife for the birth of their child.