Deep was playing in the second Test of the five-match series after India rested outstanding quick Jasprit Bumrah.
The 28-year-old took 6-99 as England, set a mammoth 608 runs to win, were dismissed for 271 on the fifth day.
Deep’s match figures of 10-147 were far and away the best of his eight-Test career.
Jamie Smith was the lone England batsman to pass 50 in the second innings, with an 88 that followed his brilliant 184 not out first time around.
A crushing victory gave India their maiden Test win in nine matches at Edgbaston, following seven defeats and a draw at the Birmingham ground.
The game was also a personal triumph for India captain Shubman Gill, who became the first batsman in Test cricket to post scores of 250 and 150 in the same match.
The 25-year-old’s majestic 269 in the first innings was followed by a dashing 161 off 162 balls in the second.
Gill has scored three hundreds in his first two Tests as captain following his 147 during India’s five-wicket loss in the series opener at Headingley, where his side dropped several catches.
India produced a much-improved fielding display at Edgbaston, as they outplayed England in all aspects.
“The way we came back with our bowling and fielding was tremendous,” said player-of-the-match Gill at the presentation ceremony.
Turning to Deep, he added: “He bowled with so much heart and skillfully with his lengths. He moved it in both directions, which was tough to do. He was magnificent for us.”
The third Test at Lord’s starts on Thursday with Gill confirming Bumrah will “definitely be back for Lord’s”. (AFP)