The 33-year-old, England's record test run scorer, made light of a poor summer with a gritty knock that appeared to be taking him towards a 33rd test century.
But after being dropped on 37 his luck ran out when he played on to Jasprit Bumrah.
Former skipper Cook was given a huge ovation as he trudged off. He could still get a chance to post another century in the second innings.
England were 134-4 in the day's final session after skipper Joe Root was dismissed for a duck three balls after Cook's exit and Jonny Bairstow followed without scoring soon after.
(Reporting by Martyn Herman; Editnig by Toby Davis)
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