Root was looking set to get a big one but a brilliant piece of fielding from Kohli saw the right-hander getting run-out for 80.
The rest of India's batting line-up failed, however, and the tourists were bowled out for 274 in reply to England's 287 as Sam Curran, the 20-year-old from Surrey, took four wickets.
It was an opening the Indians made the most of, with England reaching stumps at 9-285.
Kohli's struggles during India's last tour here in 2014 have been well documented but he made the ideal start to this series, making 149 with 23 boundaries.
The first of three wickets to fall for eight runs as he side slipped 3-216, Root's misfortune was accompanied by a full-house "send-off" from his opposite number Virat Kohli.
James Anderson was the most economical of the English bowlers with 27 runs off 15 overs though he was unlucky not to bag any wickets after an edge off Kohli was dropped when he on 21.
The India captain was running out of partners, however, as his team chased down England's first-innings total of 287.
India could strip 4 million of citizenship in northeast region
National Register of Citizens (NRC) officials check the names of the residents in the final list at a NRC Sewa Kendra (NSK). He said he was devastated to see families separated and people kept in "jails" indefinitely, some of them over many years.
"That century will have given Kohli so much confidence, not just for the rest of this match but for the rest of the series".
Indian captain Virat Kohli lets out a scream after scoring his first century in England.
Kambli recalled one of his ODI centuries back in 1996 and found similarities with the kind of celebration Kohli did on Thursday.
Overnight batsman Sam Curran (24) was dismissed this morning by Mohammed Shami.
Anderson was rewarded for his efforts with 2-41 while Adil Rashid, brought on to bowl at the tail, trapped Ishant Sharma lbw before dismissing Kohli to finish for 2-31.
He went to hospital during the lunch interval for an X-ray on his left middle finger, which he injured while fielding.
Kohli had scored two hundreds in the game at Adelaide in December 2014 but lack of support led to India losing the game by 48 runs.
It didn't help matters that England lost an early review as Anderson's loud appeal was turned down, with DRS ruling in favour of the umpire's decision.