England, who put up a gritty batting display in the second innings on the fourth day, gave up rather tamely, their last five wickets adding only 66 runs to their overnight 340 for five. They were all out for 406 at the stroke of lunch.
Captain Alastair Cook's epic knock of 176 and his 157�'run sixth�'wicket partnership with the gritty wicket�'keeper Matt Prior (91) could only prolong the inevitable, taking the match into the fifth day.
Needing 77 for a win, India raced to the target in 15.3 overs due largely to Virender Sehwag (25) and the first�'innings double centurion Cheteshwar Pujara (41 not out), who opened in place of Gautam Gambhir. Gambhir had to return to Delhi following his grandmother's death.
Left�'arm spinner Pragya Ojha was the best bowler for India, taking four wickets to add to his fifer in the first innings. While tweakers Ojha and Ravichandran Ashwin did maximum damage in dismissing England for 191 in the first innings, the visitors managed to defy the Indians in their second knock.
The seeds of the victory were sown by India's big first�'innings score of 521 for eight declared after winning the toss on a flat wicket at the Sardar Patel Stadium at Motera. Pujara batted flawlessly for an unbeaten 206, his maiden Test double�'hundred, while Virender Sehwag silenced his critics with a cracking 117, his first three�'figure score since November 2010.
England, resuming the day at 340 for five, needed to bat at least till tea to save the match. That looked unlikely when Cook and Prior were sent back by Ojha in the first hour as the pitch showed signs of deterioration with the odd ball stopping on the batsman.
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Prior went first caught and bowled one�'handed and Cook was bowled by one that kept low.
Yadav (3/70) and Zaheer Khan (2/59) complimented the spinners well by making the ball reverse in dry conditions.
Graeme Swann (17) and Tim Bresnan (20) hung on for a while with the off�'spinner playing some audacious strokes. But they did not last long, Swann bowled by Ashwin reverse sweeping once too often while Bresnan was the last man to get out, caught in the covers by substitute Ajinkya Rahane.
India are now 1�'0 in the four match series with the second game beginning in Mumbai Nov 23.