Set a target of 192 to win the Fourth Test and take an unassailable 3-1 lead in the five-match series, the hosts were at one stage cruising at 84 without loss midway through the fourth morning.
However, a flurry of wickets either side of lunch saw India collapse to 120 for five, before Jurel (39 not out) and Gill (52 not out) steadied to steer Rohit Sharma’s men to a five-wicket victory.
England will be left to rue another opportunity missed, having lost their final seven wickets for just 35 runs in their second innings when looking well set to leave the home side a daunting target.
Rohit and Yashasvi Jaiswal had made a strong start to the chase in adding 40 runs in eight overs on the third evening and continued their charge without alarm at the top of the day.
However, Joe Root made the breakthrough in dismissing danger man Jaiswal with the help of a superb James Anderson catch, before Rohit was caught behind on 55 off Tom Hartley thanks to some sharp glove work from Ben Foakes.
Shoaib Bashir, who had claimed five wickets in the first innings, then took charge, dismissing Rajat Patidar to leave India three-down at lunch and then striking again with each of his first two deliveries after the break as Ravindra Jadeja and Sarfaraz Khan fell in succession.
At that point, there were still 72 runs required and Jurel's first task was to face the hat-trick ball. Having navigated that challenge, though, the wicketkeeper offered firm resistance alongside Gill, eventually striking the winning runs after two sixes from his partner had taken the target into single figures.
