The 28-year-old Pujara was a run short of 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.
With opener Vijay for company, who was also close to reaching his own century, Pujara - not out after hitting 15 fours in 166 balls at tea - stitched a fighting 160-run stand to pilot the home team to an impressive 228 for one at the end of the second session. It was the sixth time that the duo has forged a 100-plus partnership.
Both the batsmen were lucky to have survived the session, Pujara having been given a new lease of life by DRS and Vijay escaping being caught off Stuart Broad.
But in between they showed grit aplenty against some tight and probing bowling, especially from Broad and Chris Woakes to remain unconquered after batting for nearly the entire duration of two sessions.
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.
With first Woakes and then Broad, who bowled a spell of 5-4-1-0, strangling the scoring rate at the other end, Vijay added just 7 runs in 49 balls.
He was also distinctly lucky to be grassed by debutant Haseeb Hameed off Broad at short covers when on 66. It was a drive on the up by Vijay but Hameed could not latch on to the ball after diving full length to his left.
The duo also raised a century partnership during this period of play for the second wicket in 129 minutes and 175 balls.
(REOPENS DEL 13)
The partnership was finally broken at 605 after the duo had come close to bettering the century-old all-time best eighth-wicket of 243 between Australia's M J Hartigan and C Hill of Australia set in 1908 when Yadav was stumped charging at leggie Adil Rashid who later finished with 4 for 192 after a marathon stint of 55.3 overs.
He was congratulated by the England fielders after his marathon effort that has virtually won the series for his team ahead of the Chennai game.
The Indian first innings came to an end 16 runs later to leave England with a massive task of playing for a draw on a track on which the ball spun viciously on occasions.
The entire morning belonged to Kohli and Yadav as they put paid to the England hopes of restricting the home side's lead to the minimum with forthright batting in which Yadav, playing in only his third Test, was the early aggressor before Kohli got into his stride and ripped the bowling attack with strokes all around the wicket.
Yadav had been dropped on 8 yesterday and it proved extremely costly for the visitors.
Kohli, who had made double centuries earlier this year against the West Indies in July and New Zealand last month, and his comrade-in-arm were so merciless against the visiting bowlers that runs came in a cascade, a lot many of them through boundary hits.
Kohli reached the third double century of his career when he hit Rashid to deep mid-wicket for a single exactly one and a half hours after play commenced this morning.
The landmark took him seven and a half hours to complete and he had hit 23 fours in the 302 balls he faced when he achieved the feat.
Kohli's earlier double hundreds were 200 against the West Indies at North Sound in July and 211 that he made against New Zealand in the preceding series at Indore in October.
When England batted Bhuvneshwar got rid of first innings debut centurion Keaton Jennings for a first-ball duck with an inswinger that caught the batsman in front.
Cook played across to Jadeja to be given out and the review by England also failed before the charged up left arm spinner got one to turn across the bat of Moeen to have him caught by Murali Vijay at backward short leg to end a great session for the hosts.
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