Kohli put on a marathon 226-run stand for the third wicket with Pujara (119) after the hosts lost their openers early to the England seamers.
Fit-again paceman James Anderson enjoyed his return with three wickets only to see the rest of the English attack face a tough time after the hosts opted to bat first.
Alastair Cook ready for spin Test against Virat Kohli's India
Kohli remained unbeaten on 151 and Ravichandran Ashwin was on one when stumps were called.
Kohli made full use of his reprieve on 56 when Adil Rashid dropped him at long leg off Ben Stokes to record his 14th Test century.
The star batsman mixed the right dose of caution and aggression to thwart the English bowling attack at India's newest Test venue.
Bringing up his 10th Test ton with a six off leg-spinner Rashid, the in-form Pujara tackled the English bowlers with aplomb.
Lokesh Rahul returns to India squad for England Test
Pujara, who scored 124 in Rajkot, dominated play during his 204-ball knock, laced with 12 fours and two sixes, before being caught behind off Anderson in the final session.
Kohli carried on the good work with consummate ease in the company of Ajinkya Rahane (23) who lost his cool in the penultimate over of the day as Anderson struck with the second new ball.
The batting duo stitched together a 68-run partnership as skipper Alastair Cook juggled with his bowling options.
England spinners, who gave India a run for their money in the drawn Test in Rajkot, returned wicketless in three sessions with Moeen Ali and Zafar Ansari taking a bit of a stick.
Ali though did give Kohli a scare after going for an lbw referral, but the third umpire upheld the on-field call even though the ball would have clipped the leg stump according to the ball tracker.
Cricket apart, there was drama when a stray dog forced the umpires to call tea four balls early due to it appearing from behind the sightscreen and evading attempts to chase it from the field.
There are thousands of stray dogs on India's streets, and this was not the first time one has interrupted a sporting event.
In 2011, India was forced to halt its first ever Formula One practice session when a stray dog ran onto the Buddh International Circuit.
Earlier in the day, Stuart Broad got Lokesh Rahul for nought in the second over, while Anderson accounted for Murali Vijay (20).
India handed off-spinner Jayant Yadav his Test debut with the Visakhapatnam pitch expected to turn as the match progresses.
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