The all-rounder, who could miss next week's second Test of a five-match series at Lord's because of a court trial on a charge of affray starting Monday, took two wickets in an over including Kohli.
With the match hanging in the balance, India needing 84 to win and England five wickets, Anderson had got England off to the flawless start with the wicket of Karthik (20) with the sixth ball of the day, Dawid Malan going some way to making up for his three dropped catches in the match with a low grab at second slip.
But fellow England all-rounder Sam Curran was named man-of-the-match after starring with both bat and ball.
Kohli lamented his team's batting - having scored 200 of their 436 runs across two innings, the India captain was well within his rights to do so - and was impressed by England's spirit in a rollercoaster of a Test match.
In the second innings, Kohli was undone by a Stokes' inswinger while batting on 51 on Saturday, in chase of 194.
"I am proud to be part of his group". Curran stood out as he took the attack to the opposition bowlers by going after them.
Stokes eventually claimed Pandya's wicket to hand England the win in what proved to be a compelling Test match.
"It was a great surface that made for some great Test cricket and I think it's important that you don't underestimate how well people have bowled on there", said Root. "I thought we did pretty well".
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"If we pull ourselves together, and even play 80-85 percent of the cricket we can, then it s going to be a very exciting and competitive series".
Meanwhile Kohli urged India to remain "positive and fearless" during the rest of the series. For all the blistering big-hitting of the white-ball game, the way the momentum shifted from one day to the next at Edgbaston, culminating in a gripping final session, underlined that nothing in cricket can beat the drama of a hard-fought Test. "A team like England doesn't let you do it everyday, they were relentless and they made us work very hard for our runs", said Kohli. Hopefully we will build on that. "We have to play positive and fearless". And 17 Test matches have been played against Sri Lanka, Pakistan and India without the hosts once tasting defeat.
Given the sunny conditions in Birmingham, the only certainty then was the match would finish with more than a day to spare. In a shaky start, India lost five batsmen before skipper Virat Kohli (43) and Dinesh Karthik (18) combined for a crucial unbeaten sixth-wicket partnership.
It might be too simple to say "get Virat Kohli out and you get India out" but perhaps not by too much.
It was by design that England limited Kohli to nine deliveries in eight overs at the other end, but a straight-driven four by Pandya off Stuart Broad indicated he had found a plausible new partner.
India pace bowler Ishant Sharma took 5-51 - including three wickets in an over - to undermine England's second innings.
Despite getting the right result yesterday, England have chose to call up Ollie Pope, the Surrey Batsman, to the squad in place of Dawid Malan for the second Test against India at Lord's, starting on Thursday.