Ravindra Jadeja, the hosts' arch rival after the Trent Bridge spat with James Anderson - yet to play out in a high-stakes International Cricket Council hearing - made his presence felt again to leave England needing their highest run chase at HQ.
To avoid a 10th Test without victory, England were required to replicate their first-innings 319 after Jadeja's career-best 68 from No.8 - and yet another half-century from tailender Bhuvneshwar Kumar (52) - helped India to 342 all out.
By stumps on day four, on a pitch providing all bowlers with increasingly variable bounce and Jadeja sharp turn out of the rough, opener Cook looked a spent force as England limped to a precarious 105 for four.
The equation was much more favourable when the tourists were 235 for seven, having just lost Murali Vijay for an impressive 95. But Joe Root dropped Kumar on two, and he and Jadeja punished England in a stand of 99 - especially in 10 overs after lunch which yielded 66 runs.
Jadeja seized the moment, unsettling England by charging the second new ball and scampering extra runs between seven boundaries in his 42-ball maiden Test 50. It was Anderson who finally accounted for Vijay, and before then Liam Plunkett (three for 65) who got one in the right spot to MS Dhoni for Ian Bell to take a neat catch at second slip.
That ended a stand of 79 with opener Vijay, the India captain gone for an uncharacteristically stoic 19 off 86 balls. When Cook then took a very good, 'pressure' catch - running back and diving from mid-off with the ball steepling over his head off Moeen Ali - Stuart Binny's counter-attacking intent had come to nought.
Jadeja, demoted a position, immediately went after Moeen - and runs came quickly as the left-hander took on his old adversary Anderson too. Vijay played perhaps his first false shot, to the 247th ball he faced, when he edged behind.
But Jadeja began advancing against Anderson - and after Kumar's escape, Root missing a very sharp chance off Stuart Broad at fourth slip, he played the perfect foil. Even after Jadeja fell to a mis-pull at Ben Stokes (three for 51) and another fine catch from Cook running back again, this time from slip, Kumar stayed to complete his third half-century in four innings.
In a number of several thorns in England's side, Kumar is perhaps the more irksome - having also taken six wickets in the first innings - and by the time he was last out, he had ensured a major challenge remained after all for Cook and his men.
A Dhoni hunch soon undermined England's prospects of bettering the 282 for three they made to beat New Zealand here 10 years ago. He introduced Jadeja's left-arm spin, for only the seventh over of the innings, and was rewarded with a wicket first ball.
Jadeja hit Sam Robson's front pad marginally in line with off-stump, with an arm ball, and Kumar Dharmasena decided lbw was in order.
Cook was batting perhaps for his future as captain, and found an ally in first-innings centurion Gary Ballance for a stand of 58. The two left-handers had to be highly-skilled and concentrated to deal with Jadeja especially, with a gaggle of leg-side catchers, on a wearing pitch with claustrophobic cloud cover and thunderstorms passing close by.
They coped admirably in a fascinating passage of play until another bowling change again brought an immediate dividend. Ballance played at the first delivery from the returning Mohammed Shami - and edged behind. It was to be the first of three wickets for two runs, Ishant Sharma taking the others without conceding as Bell was bowled off-stump playing defensively inside a delivery which kept low and Cook himself forward and edging behind.
He had spent more than two hours and 93 balls trying to get himself out of a wretched run but could muster only 22 runs to take his sorry annual tally to 129 in nine innings.
England still had live batting resources, starting with Root and Moeen, yet Cook walked off with the resigned air of a captain who understandably feared this match might just be ebbing away.