Insipte of losing two set batsmen in Cook (190) and Jonathan Trott (87), England were comfortably placed at 381 for three in their first innings, a lead 65 runs over India, at tea.
Kevin Pietersen (29 not out) and Ian Bell (3 not out) were unbeaten at the crease at the break.
Resuming the day at 216 for one, England rode on a 173-run second wicket partnership between Cook and Trott, who returned to form with a brilliant 87, to pile on the misery for India.
Captain Cook's record-breaking eight-hour-and-12 minute innings finally came to an end in a freak manner when he was run out by a direct throw from Virat Kohli.
While backing up from the non-striker's end, Cook was caught short off the crease by Kohli's direct shy at the stumps.
Cook faced 377 balls during his record-breaking knock and hit 23 boundaries and two sixes.
As he was approaching his third double century, Cook slowed down a bit while India kept attacking Pietersen at the other end.
