India finished third day's play at 451 runs for the loss of seven wickets.
Kohli and Jayant Yadav (30*) are currently at the crease, trying to give India a bigger lead against the visitors.
Kohli hammered 17 boundaries in his knock as he completed his 15th Test century here.
Earlier, Vijay hit 10 boundaries and three sixes in his 282-ball knock that dragged India out of trouble after Cheteshwar Pujara (47) departed early in the day.
Adil Rashid,Joe Root and Moen Ali have picked up two wickets each for England.