The 28-year-old Pujara stuck his ninth century in his 39th Test after he was reprieved on 86 by the Decision Review System which is being used by India at home for the first time.
The Saurashtra batsman survived a few nervous minutes going into the tea break, spending eight balls on 99 before the teams went in for the break.
While, Vijay, who survived a leg before the wicket shout in the last over before lunch against Adil Rashid, also played superb knock to completed his century.
They had come together at the fall of opener Gautam Gambhir off the first ball of the second over today morning when India were on 68, having added just five to their overnight score.
Earlier, England won the toss and elected to bat on first day scored a total of 537 runs with help from three centuries.
On first day, Joe Root scored a ton while Moeen Ali finished with unbeaten 99 at stumps. On the second, Moeen completed his century but the surge for England total was by Ben Stokes who scored 128 runs and added some valuable runs with the tail.
It is the first time since 2012 that a visiting team has crossed the 500-run mark in India.