Cook (190) laid the painstaking foundation in a stand of 173 with Jonathan Trott (87) for England to try to push for victory and establish a 2-1 series lead over the final two days. But after he was run out in bizarre circumstances, Kevin Pietersen fell for 54 before he could provide the necessary acceleration to put India under optimum pressure.
It therefore fell to others to chip England towards a stumps total of 509 for six in reply to 316 all out on a pitch just beginning to show signs of wear, with variable bounce and sharper turn offering second-innings promise to bowlers of all persuasions.
Cook's eight-hour epic was finally ended by a fielder, when Virat Kohli arrowed in a direct-hit throw from midwicket to run him out backing up. Cook appeared in position to ground his bat in time, only to raise it and allow the ball through. His own reaction told the tale, however, that he was not forced into protective evasive action but merely for once guilty of a rare human error.
The second-wicket pair of Cook and Trott continued remorselessly on Friday morning, although Cook needed one significant piece of good fortune on 156 when Ishant Sharma put down a straightforward return catch.
India managed to apply the brakes either side of lunch but could not manage a breakthrough as Trott moved past his 131-ball half-century, with a leg-glance off Zaheer Khan for his seventh four - a shot which also brought up the hundred stand. Spin replaced pace and Trott was eventually undone by one that turned from Pragyan Ojha and edged behind.
Pietersen's arrival brought a familiar change in the bowling, Mahendra Singh Dhoni summoning Yuvraj Singh to try his luck against his favourite sparring partner. Save for an early mistimed cut into the ground and just past off-stump, however, Pietersen was unfazed.
Instead, it was Cook who finally showed some frailty - surprised perhaps by an Indian fielder excelling himself in a match when that has so rarely happened so far. Thanks largely to Cook's 23 fours and two sixes, England were in any case already handily in credit with power to add.
After tea, Pietersen duly hit Ojha for three off-side fours off the first three balls of the session. But Plan A was compromised when Ian Bell got an under-edge behind off Sharma; then Pietersen was lbw sweeping, immediately after reaching his 83-ball 50, to give Ravichandran Ashwin his only wicket at a cost of 183 runs.
Samit Patel hinted at the extra impetus required until Ojha found extra turn to have him very well-caught by Virender Sehwag, moving quickly to his right at slip to knock up an edged cut and collect the rebound. In Matt Prior and Graeme Swann, though, England still had the right men for the occasion to bolster the lead to 193 by the close.