At tea, Cook was unbeaten on 138 and Matt Prior was giving him company at the other end on 40 with England still trailing India by 66 runs with five wickets remaining in their second innings.
The duo had an unconquered partnership of 65 runs for the sixth wicket.
England were following on 330 runs behind the hosts' after collapsing for 191 in the first innings in reply to India's mammoth 521 for eight declared.
After lunch break, two more English wickets fell with pacer Umesh Yadav picking up both the wickets in successive balls though he failed to take a hat-trick at Sardar Patel Stadium here.
Yadav struck two body blows by making the 76-over old ball reverse swing to trap Ian Bell and Samit Patel leg before wicket off the fifth and sixth balls of his first over of a new spell to leave the tourists gasping at 199 for 5 in the first hour of play of the post-lunch session.