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.
In Image: India's Virat Kohli shakes hand with England players after winning the first Test
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