Kohli also farmed the strike brilliantly during a tenth-wicket stand of 57 with Yadav, who faced 16 balls for his unbeaten one.
Asked to rate this knock, Kohli put it second on the perch behind his second innings effort at Adelaide in late 2014 where he scored 141 and nearly pulled off a chase of 364. At 216/3, England looked firmly in control. That the match was still alive last night owed plenty not only to Malan's drop of Kohli which he will need no reminding cost England over 100 runs and kept India in the game, but to the spirit shown by Curran. Root however, wasn't the quickest to the non-striker's end, and fell short of his crease as his Indian counterpart pulled off a brilliant collect-and-throw - all in one quick motion - and effected a direct hit. But keeping his head high, Indian skipper Virat Kohli cheered for the game than letting the spirit down for the remainder of the series.
Making the most of the two dropped catches by England at 21 and 51, Kohli let out a huge roar in celebration after belting the ball off Ben Stokes for a boundary to bring up his century.
"I had goosebumps listening to the Barmy Army chants and that first hour tomorrow (Saturday) is going to be crucial", Curran said.
It was the second time in the match that Ashwin had dismissed Cook, England´s all-time leading Test run-scorer, this way.
The sun was out at Edgbaston but the ball was doing enough to trouble the batsmen. India saw a couple of edges not getting into the hands of the fielders. In first session, we should have a result.
Curran, after receiving the Player of the Match award, said that he learned a lot from batting Kohli bat.
Kohli said his main aim here was to take the total as close to England's 287 as possible.
Ishant Sharma picked up 5 wickets for 51 runs
India have always been criticised for their poor close catching but England, with the tourists still on 100 for five, dropped two slip chances of their own, with Malan reprieving Kohli off Anderson.
The hosts drew first blood in the five-match series with a 31-run win at the Edgbaston.
Curran had come to the wicket at 80-6 after Stokes had followed Jonny Bairstow and Malan into the final column of Ishant Sharma's analysis just before lunch.
He batted for almost five hours and faced 225 balls, including 22 fours and a six. England did not have to wait long for their first breakthrough as Broad (2/29) trapped Murali Vijay and then removed Shikhar Dhawan (13) caught behind.
The 20-year-old cashed in on that opportunity.
India were 141 for six, needing 53 more runs to win, when paceman Stokes had Kohli lbw for 51 with just his third ball of the day. Kohli, though, managed to overcome the tough period to register his maiden Test hundred in England. "It is easy to make an emotional decision right now, but we need to sit outside and decide for Lord's depending on the surface", the 26-year-old said. Karthik goes for 20.
India now looked to Pandya and Ishant Sharma to take them to just their seventh win in 58 Tests in England. With Cook disappointing yet again in the dying minutes of the day, England will have to count once again on Joe Root playing the anchor's role and building partnerships around him.