The 30-year-old left-handed opener started England’s reply to New Zealand’s first innings 350 on Saturday needing just 32 more runs to surpass Gooch’s mark of 8,900 runs in 118 Tests.
Cook, first coached by ex-England captain Gooch as a schoolboy, reached lunch unbeaten on 27.
Then, to his 13th ball after lunch Cook passed Gooch– whose runs came in four more Tests (118 to 114) – when he square-drove Tim Southee for four to break a record that had stood for nearly 22 years.
Scores at 75.0 overs (Day Two)
New Zealand 1st Innings 350 (72.1) (L. Ronchi 88, T. Latham 84, M. Craig 41, Broad 5-109 )
England 1st Innings 215-2 (A. Lyth 107, A.Cook 75 )
Former England batsman Derek Randall, Cook’s coach at Bedford School, North of London, told BBC Radio’s Test Match Special: “You can imagine as a cricket coach, to have the pleasure of working with somebody like Alastair Cook is very special.
“The first time I saw him on the bowling machine, I couldn’t believe the balance and timing he had. He’s a lovely lad, a very special boy.”
Cook was eventually out for 75, lbw to off-spinner Mark Craig on the sweep after the tourists overturned Indian umpire S. Ravi’s original not out decision to end a first-wicket stand with Adam Lyth worth 177.
The skipper batted for nearly four hours and faced 187 balls including 12 fours.
Cook, speaking on Thursday, insisted he was nowhere near Gooch’s class as a batsman and tried to play down the significance of the landmark.
“It would be a lovely moment. I wouldn’t put myself anywhere near in his class but it would be a great moment,” said Cook.
“If I’m lucky enough to get that it will be a moment I’ll remember but if I am 30 not out it’s important in a game situation I go on and get a big score,” added the left-handed Cook, like the right-handed Gooch an Essex and England opening batsman.
Cook added: “I wouldn’t be here, or anywhere near here, without Goochie’s help, so it will be slightly strange if I do go past his record because without his hard work and dedication to me and my game, I wouldn’t have scored half the runs I would have done.
“It’s a bit of a strange one. But there will only ever be one Graham Gooch. He’s England greatest-ever batsman.”
By going past Gooch, Cook moved up to 13th place on the all-time list of leading run-scorers in Test cricket, where retired India great Sachin Tendulkar remains way out in front with 15,921 runs in 200 matches.