Kohli and Pujara shared a stand of 226 runs for the third wicket after India lost openers' early.
Captain Virat Kohli and Cheteshwar Pujara made centuries and shared a stand of 226 to put India on course for a big first-innings total against England on the first day of the second Test on Thursday.
Kohli was unbeaten on 151 and Ravichandran Ashwin on one as India reached 317 for four at the close after winning the toss in the first ever Test match in the port city of Visakhapatnam.
On a surface expected to assist the spinners from early on, Kohli had no hesitation in batting but his plans suffered an early jolt.
Fit-again opener Lokesh Rahul lasted just five deliveries as fast bowler Stuart Broad dismissed him in his first over.
Rahul fell for a duck, hanging his bat away from his body to edge Broad to Ben Stokes at the third slip.
His opening partner Murali Vijay looked in good touch, hitting four crisply driven boundaries in his 20 before he fell to James Anderson.
England's highest Test wicket-taker bowled cross seam to extract steep bounce and hit Vijay on his glove for Stokes to complete a simple catch.
The wicket marked a successful return for Anderson, who had not played since August with a shoulder injury and replaced fast bowler Chris Woakes in the side.
The hosts were struggling on 22-2 when Kohli and Pujara came together.
The right-handed pair had few problems in negotiating the English bowlers and their only moments of concerns in the first session were a couple of run-out opportunities.
England did not manage to separate the pair before tea, which was taken few minutes earlier after a stray dog ran on to the field and held up play.
Pujara survived a England review for leg before against Moeen Ali and brought up his 10th Test hundred with his second six off leg-spinner Adil Rashid.
"The way we are placed at the moment, I think anything above 500 will be a good total for us," Pujara, whose ton was his third in as many Tests, said.
"We would like to put up a big total and hopefully won't have to bat again."
Playing his 50th Test, Kohli, who was dropped on 56 at fine leg by Rashid off Stokes, pushed Anderson through the covers to register his 14th hundred.
Cook tried everything to separate the duo, including asking his bowlers to operate with eight fielders on one side to stem the flow of runs and frustrate the batsmen.
Anderson returned to finally break the partnership when Pujara was out on 119 after getting a thick edge to wicketkeeper Jonny Bairstow.
Kohli then added 68 for the fourth wicket with Ajinkya Rahane before the latter was out for 23 to give Anderson his third scalp. None of England's spinners managed a wicket on the first day.
