Victory saw England level the five-match series at 1-1 after India's 151-run win in the second Test at Lord's.
India, 215-2 overnight in their second innings, collapsed against the new ball, losing eight wickets for 63 runs in 19.3 overs on Saturday with Ollie Robinson taking 5-65.
India's 278 all out, however, was 200 runs more than their woeful first innings of 78 — made after captain Virat Kohli won the toss — which saw England great James Anderson rip through the top order with 3-6.
The tourists resumed on Saturday on 215-2 but, with 80 overs bowled, England took the new ball straight from the start of Saturday's play.
From the moment Cheteshwar Pujara was lbw to Robinson without adding to his overnight 91, lbw playing no shot to Robinson, England were in complete command on Saturday, with Kohli falling soon afterwards for 55 — his first fifty of the series.
The match was a personal triumph for England captain Joe Root, who top-scored with 121 out of a total on 432 on his Headingley home ground.
It was Root's third century of the series and sixth of the calendar year.
Meanwhile, the rest of England's often fallible top order all posted fifties, with Dawid Malan compiling 70 on his Test recall after Dom Sibley was dropped from the team.
The fourth Test at the Oval starts on Thursday.
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