After he was the last man out with about 30 minutes left of the day, Kohli was given a standing ovation around Edgbaston, with England fans also showing their appreciation of one of cricket's box-office talents.
English cricket team reached a milestone on 1 August becoming the first team to play their 1,000th Test match in the 142-year history of Test cricket.
His last-wicket stand of 57 with Umesh Yadav - of which the number 11 contributed only one run - was full of clean hitting from Kohli, who launched Rashid over long-on for six before finally falling as he slapped the leg-spinner to Stuart Broad at point.
The opening batsman of India, Shikhar Dhawan along with Murli Vijay added first fifty partnership of Indian innings.
Virat Kohli had an "informal chat" with match referee Jeff Crowe ahead of day three of the first Test between England and India to discuss his responsibilities and behaviours as captain, Sky Sports understands.
Kohli's superb shepherding of the tail took some of the gloss off what was an otherwise impressive performance from the England attack, particularly during a thrilling afternoon session. However, the prized wicket of Alastair Cook late in the day put the smile back on Kohli's face. "I think to a larger extent that particular thing of doing something in the air is something I consciously worked on", he said. Kohli survived an arduous spell by James Anderson and Ben Stokes to hold the Indian innings together.
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Lokesh Rahul dispatched his first ball to the boundary but dragged his second from Curran on to his stumps.
Kohli, though, managed to overcome the tough period to register his maiden Test hundred in England. Curran's three-wicket burst in eight balls reduced India to 59/3 in no time even as Rahane joined his captain to sneak in a few singles before heading for the break.
Curran is an exceptionally promising all-rounder but he was certainly not guaranteed a place in the XI and may not have featured if England had more faith in the fitness of Mark Wood and Chris Woakes.
England batsman Jos Buttler went to the hospital during the lunch interval for an X-ray on his left middle finger, which he appeared to injure while fielding.
Under cloudy skies, on a damp pitch and against a moving ball, Indian captain Virat Kohli played perhaps his best Test innings his bright career so far. And I had total clarity that we are going for the target.