Earlier, starting at the overnight score of 124 for 2, India had ideal conditions for batting on a humid and warm day and Kohli and Pujara looked to grind and play for time with no hurry whatsoever.
The irony was that England had enjoyed a solid opening stand to be 54 without loss.
They set England an nearly impossible 521 to win the match after captain Virat Kohli scored a second innings century in India's 352 for 7 declared.
It wasn´t until Monday´s 41st over that India lost their third wicket, with Pujara edging recalled all-rounder Ben Stokes to first slip Cook.
Since 2014, when Anderson dismissed him four times, Kohli has faced 325 balls from him in Test cricket, home and away, and scored 155 runs without being dismissed.
Only Jos Buttler's 39 briefly kept India at bay.
Cook edged paceman Ishant Sharma to give Pant an easy first Test catch. However, the England opener was not able to catch the ball.
Kohli was not at his most fluent but this was an ideal innings given India´s situation and an edged four off Chris Woakes, his 10th boundary in 191 balls during almost five hours at the crease, saw the star batsman to a 23rd Test hundred.
All-rounder Pandya took five wickets for 28 runs in six overs, including four for eight in 11 balls, as he revelled in the swing-friendly conditions.
Ben Stokes, recalled just days after being acquitted of an affray charge on Tuesday following an incident outside a Bristol nightclub in September past year, walked out to a few boos from the crowd.
If England, who lead the five-match series 2-0, are to salvage anything from this match, they must pull off the highest fourth-innings run-chase in Test cricket, or bat for two more days to earn a draw.
England were now 118 for seven.
However England should have had Kohli out in the 90s for the second-straight innings.
Virat Kohli tried to play a cover off Adil Rashid but could not get his timing on the shot.
Buttler, with just last man James Anderson for company, hooked and drove sixes off Shami and Sharma respectively before he holed out off Bumrah.
Kohli was still on his tea score of 93 not out when his edged drive off an outswinger from Anderson, armed with the new ball, burst through Jennings´s hands in the gully.