After bundling out India for 316 in the first session, England openers played responsible innings to lay a solid platform.
At break, Nick Compton (41 not out) was giving Cook company at the other end.
Except for being dropped at the first slip by Cheteshwar Pujara off the bowling of Zaheer Khan when he was on 17, Cook did not have any trouble negotiating the Indian attack on his way to his third half-century of the series.
Indian bowlers tried hard to give their team a breakthrough, even as skipper Mahendra Singh Dhoni kept on rotating them. But the English openers' cautious approach paid rich dividends as they managed to put on a 100-plus run partnership.
This is Cook and Compton's second century-plus opening partnership in the series.
Cook, during his innings before tea, also completed 400 runs in the series that included two centuries -- 176 (Ahmedabad) and 122 (Mumbai).
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Earlier, despite a fighting half-century by Dhoni, England could restrict the hosts to a modest total on a batting-friendly flat Eden track.
Resuming on 273 for seven, overnight batsman Dhoni, starting on 22, went on to hit 52 off 114 balls with the help of five boundaries and two sixes to help India cross the 300-run mark.
But Monty Panesar's two wickets in the first five overs of the day enabled England to dictate terms.