However, it was also notable as Kohli's 23rd ton saw him go past Mohammad Azharuddin's tally of 426 runs to become the Indian captain with most runs in a series in England.
Only Jos Buttler´s 39 kept India at bay and denied Kohli the chance of enforcing the follow-on.
India were in firm control of the third test against England as they advanced to 194 for two at lunch on the third day, building up a commanding lead of 362.
Both fell shortly after the break, however, with Ishant Sharma once again removing Cook, who edged behind to wicketkeeper Pant.
New batsman Ollie Pope fell for 10 when a genuine glance off Sharma was well caught down the legside by the 20-year-old keeper.
He made 119 in the first innings of the Johannesburg Test in 2013 against South Africa before being dismissed for 96 in the 2nd innings.
Broad cleaned up Ravichandran Ashwin in his next over, before James Anderson dismissed Mohammed Shami and Jasprit Bumrah in consecutive deliveries to wrap up the innings.
England were now 118 for seven.
That left England needing a mammoth 521 for victory, albeit with more than two days to get the runs.
Kohli, who had recovered from a stiff back to play in the Test, batted nearly six hours (293 minutes) before he fell leg before to Chris Woakes after tea on the third day with England's bowling wearing a beaten look.
They got them when Buttler´s leading edge off Shami just cleared Ajinkya Rahane at cover-point.
Pandya's five wickets came in 29 balls, only bettered by Harbhajan Singh's five wickets in 27 balls against Windies at Kingston in 2006.
But they were still well-placed thanks to Saturday's fourth-wicket partnership of 159 between skipper Virat Kohli (97) and vice-captain Rahane (81).
India´s openers put on a brisk 60 before Rahul (36) deflected a drive off Stokes onto his stumps and Shikhar Dhawan (44) was stumped by Bairstow off leg-spinner Rashid.