Cook paired with Matt Prior to stage a defiant stand of 141 not out as England look to salvage an unlikely draw in the first Test.
England ended the day on 340-5, 10 runs ahead of India's first innings total, and Gooch believes that Cook's first Test as permanent captain has brought out the best in the left-hander.
"Some players blossom under the captaincy as a performer, and he has certainly blossomed under that responsibility here," said Gooch.
"It was great commitment from our guys and great fighting spirit. There was belief in their own ability, and Alastair led from the front as captain. That will do him the world of good to put that score on the board, showing what he is capable of and what this team is capable of.
"I think that was as good an innings as I've seen him play, because he was under great pressure after a poor first-innings performance from the team."
Cook's century puts him one ahead of Gooch in England's list of most prolific centurions.