Kohli scored 115 in the first innings as India posted 444 in response to Australia's 517 and in the second innings, the visitors were given a target of 364 in 98 overs.
But Kohli's superb 149 took the tourists to 274 all out, just 13 runs adrift of England´s 287.
Root did at least bag one notable career milestone, displacing Alastair Cook as his country's quickest to 6,000 Test runs when he reached 40.
In doing so, Stokes become the eighth Englishman to complete the double of 2,000 runs and 100 wickets in Test cricket.
For India, star off-spinner Ravichandran Ashwin took four wickets while Mohammad Shami took two wickets.
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That's not to say Kohli was making light of the hard slog at Edgbaston: "I am very happy".
It looked as if the day might belong to Surrey left-arm swing bowler Sam Curran. Sixth ball fetches WICKET!
"Personally, it was obviously a pretty special day for me with the ball", said Curran.
"Credit to a great innings there", said Curran. "You can see that he's going to play well when he's got that sort of intent, he's got that arrogance about him because he knows he's a little bit if not a lot better than his teammates or anybody else in the world at the moment when he's in this form".
Kohli, one of the outstanding batsmen of his generation, managed just 134 runs in five Tests at an average of 13.4 on his maiden tour of England four years ago.
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England seamer Sam Curran praised India skipper Virat Kohli's innings on the second day of the first Test at Edgbaston.
He continued to punish the England bowlers to notch up 22 boundaries and a six during his 225-ball knock.
Kohli also farmed the strike brilliantly during a tenth-wicket stand of 57 with Yadav, who faced 16 balls for his unbeaten one.
"Coming on and taking a few early wickets, I can't really remember it, it was so unreal".
Such was the dominance of the 29-year-old captain, the next top scorer for India was opener Shikhar Dhawan with 26.
That was the last delivery of the over and the next ball saw all-rounder Hardik Pandya missed on nought when Cook dropped a routine first-slip chance off Stokes.
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Red Devils teammate Ander Herrera is backing the Martial to turn the corner very soon. Now it's all about work, confidence, about keep playing like he did today.
Ben Stokes had his head in his hands after Kohli was dropped.