The 25-year-old Nair from Rajasthan blasted 11 fours and one six in his 217-ball unbeaten innings to complete a well-deserving hundred and shared a 63-run partnership with Murali Vijay at the MA Chidambaram Stadium.
At the lunch interval, Ravichandran Ashwin (9) was giving company to Nair (122) at the crease with India trailing by just 14 runs and having 5 wickets in hand in their first innings. England had scored 477 in their first essay.
Vijay (29), who had come down the order at No. 6, was the only batsman dismissed in the session as Liam Dawson picked up his maiden wicket in the 124th over after trapping him in front of wicket.
Earlier, resuming at an overnight score of 391-4, Nair and Vijay found the going a bit tough against the duo of Dawson and Stuart Broad.
While Dawson bothered Vijay with his slow deliveries in the 110th over, Broad almost had his man in the 115th over when he induced a slight nick off the Tamil Nadu batsman but umpire Simon Fry felt otherwise and England didn't have any reviews left.
In the next over, Nair blasted Dawson for a six over long-on, while Vijay picked up a boundary off Ben Stokes behind point in the 121st over.
One over later, Nair sliced Stokes behind point to pick up another boundary and along with it his maiden Test century and he celebrated the achievement by raising his bat.
Vijay's fall in the 124th over brought Ashwin to the crease and after a few overs, Nair once again repeated his treatment to Stokes, picking up successive boundaries off the bowler to keep the scoreboard ticking.
Ashwin picked up his first boundary when he late cut a Dawson delivery behind point. Just before lunch, Adil Rashid was introduced into the attack and Nair hit him through extra cover as India took lunch after the 135th over.