India capitulated inside 30 overs in another feeble batting display, Chris Jordan taking four wickets for the hosts after Joe Root's unbeaten 149 had put England in complete control of the match.
It was a sweet moment for England captain Alastair Cook whose job was under serious threat after suffering a humiliating loss in the second match against India at Lord's, the team's 10th successive test without a win.
"It was an amazing turnaround after Lord's, the players and the new coaching staff have made a lot of difference," a beaming Cook told reporters.
"India crumbled at the end but that was from the relentless pressure."
Led by Root, England plundered 101 runs in rapid time on the third morning and they picked up the wickets of openers Murali Vijay and Gautam Gambhir to leave India tottering on nine for two at lunch.
Vijay was trapped lbw by James Anderson for two and Gambhir, looking for a non-existent single, was run out by a direct hit from Chris Woakes after being sent back by Cheteshwar Pujara.
The procession continued after an interval extended by a rain delay.
Pujara edged a catch to wicketkeeper Jos Buttler to give Anderson his 380th test wicket, three behind the English record held by Ian Botham.
Ajinkya Rahane was brilliantly caught one-handed by a diving Gary Ballance at third slip off Stuart Broad and MS Dhoni, so often India's saviour in this series, was caught by Sam Robson at short leg off Woakes to leave India in disarray at 46 for five.
Virat Kohli's miserable run continued when, on 20, he edged Jordan to Cook at first slip and Ravichandran Ashwin was caught by Ian Bell at second slip off Jordan after Ballance had pushed the ball up.
Bhuvneshwar Kumar edged Jordan straight to Bell and Varun Aaron failed to beat Moeen Ali's throw from the boundary and was run out trying to make a needless second run.
SIMPLE CATCH
Jordan had the final say to complete figures of four for 18 when a vicious short ball forced Ishant Sharma to loop a simple catch to Moeen, leaving Stuart Binny 25 not out and the top-scorer in the innings.
"The last three tests, we were not up to the mark. We never competed," Dhoni said.
"Today's batting was a reflection of a loss of confidence. It's disappointing. The youngsters will have learned, not many will have played here. It's important for them. Right from the start, our batsmen haven't performed."
England had torn into the Indian attack after resuming on 385 for seven.
Root clipped Sharma for three through mid-wicket to reach his fifth test century, celebrating with a leap in the air and flamboyant fist pump.
Jordan, on 20, edged a fierce Sharma delivery through to wicketkeeper Dhoni to end an eight-wicket partnership of 82 from 76 balls.
Broad threw his bat at everything and raced to 37 off 21 deliveries, including a six and five fours, before he gloved a short ball from Sharma to Kohli at third slip.
Root continued to plunder the wayward attack and struck a succession of boundaries all round the wicket.
Anderson was lbw to Ashwin for one to end the carnage and Root was left unbeaten on 149 from 165 balls, including a six and 18 fours.
"It's always nice to score runs but to finish the way we have was very pleasing," Root said.
"To bounce back the way we have has shown a lot of character, the guys had to dig deep."
