England claimed five India wickets in the final session to win the historic 2,000th Test and draw first blood in the four-match series at Lord's.
James Anderson (5-65) was once again the England hero, claiming his 11th five-wicket haul and third at the home of cricket to help dismiss India for 261 and with 28.3 overs to spare.
The outcome of the match was hanging in the balance heading into the final session, however Anderson and Stuart Broad (3-57) teamed up with devastating effect to complete a significant victory.
Suresh Raina (78) battled hard for India, but when he became the ninth wicket to fall England wasted little time wrapping up an emphatic 196-run victory.
Attention now turns to the second Test at Trent Bridge on Friday, where India will be sweating on the fitness and health of a number of their key players.
India resumed the final day in front of a packed-out crowd on 80-1, and Anderson found VVS Laxman's edge with the last ball of the second over, but the edge flew safely into the large gap between second slip and gully.
Chris Tremlett sent down a superb over to first-innings centurion Rahul Dravid, beating him twice on the outside edge and forcing a bat-pad chance. Ian Bell did well to get a hand to the ball at short-leg but could not cling on.
Anderson made the breakthrough in the eighth over, tempting the usually cautious Dravid into a loose dab outside the off stump. The ball did just enough to snare the edge and Matt Prior took a simple catch to see off 'The Wall' for 36.
Umpire Billy Bowden then found himself in the thick of things, turning down huge appeals first for lbw against Gautam Gambhir and next for caught behind against Laxman.
Replays indicated the first decision was correct but the 'snickometer' - which cannot be used in DRS referrals - appeared to back Broad's decision to review the second.
Strauss opted for some puzzlingly defensive fields but, having moved past 50, Laxman helped the England captain by turning an innocuous Anderson short ball straight to Bell at mid-wicket for 56.
Swann dismissed Gambhir (22) leg before in the following over, taking the score to 135-4 and bringing Tendulkar to the crease for his second rousing ovation of the game.
Anderson almost wrecked the script when he speared one through the gate first up, but Tendulkar moved to seven at lunch, with England in command.
England captain Strauss' torrid match in the slip cordon continued when he failed to hang onto a regulation chance to remove Tendulkar soon after the break, but Anderson returned two balls later to pin the 'Little Master' in front of the stumps for only 12.
England sensed blood and Prior, whose wonderful 103 not out on day four gave his side such breathing space, was desperately close to stumping Raina six balls later.
After just managing to slide his foot back behind the line, Raina and captain Mahendra Singh Dhoni dug deep to reach tea on 218-5 and with the left-hander past 50.
The draw looked the favourite result at the interval, but, with 40 overs to go, England reignited their hopes of victory with the key wicket of Dhoni.
Dhoni and Raina had batted together for 18.2 overs before the India captain tamely edged Anderson through to Prior early in the final session.
That wicket spurred on both the home crowd and players and in the 91st over Broad could, and perhaps should, have dismissed both Harbhajan Singh and Raina in quick succession.
First, a nasty short ball from Broad found Harbhajan's top-edge, however the ball simply looped over the slip cordon for two runs.
There was more anguish two balls later when Eoin Morgan grassed a simple chance at backward point with Harbhajan on 11, and Broad's mood worsened when umpire Bowden turned down a huge lbw appeal on Raina the following ball.
With England fired up and feeling incredibly hard done-by, Anderson eased the frustration by claiming the seventh India wicket in the following over.
Harbhajan, who adopted an "attack is the best form of defence" strategy, chanced his arm once too often and simply spooned his attempted pull shot off Anderson to Tremlett at mid-on.
Broad then roughed Praveen Kumar up before rattling back his middle stump and Anderson put England on the brink of victory when he found Raina's edge and Prior did the rest.
With a famous win in sight, England wasted little time recording their first Test match victory over India on home soil since 2002 when Broad trapped Ishant Sharma in front of middle stump.