Starting as 4-7 favourite, Stradivarius looked short of room approaching the final furlong but jockey Frankie Dettori produced a stunning change of gear to move the six-year-old past runner-up Nayef Road and Santiago, who finished third.
Stradivarius, trained by John Gosden, had to carry 15lb more than the Irish Derby winner Santiago under weight-for-age rules.
"What a horse, giving 15lb away. Everybody rode to beat me and he still gets out and wins. What can you say, he's an amazing horse," Dettori told ITV Racing.
"What he has done he's broken records - well done to Bjorn Nielsen, the owner-breeder."
Stradivarius' win eclipsed the three Goodwood Cups won by Double Trigger (1995, 1997, 1998).
It was Dettori's second major triumph in a matter of days after guiding Enable to victory at the King George VI and Queen Elizabeth Stakes for a record third time at Ascot on Saturday.
"You go from a superstar like Enable to an absolute champion like this horse in three days. It's the stuff of dreams," he added.
"I know I've got a good partner and I just had to be patient. When you've got good horses the gaps will come." (Reporting by Hardik Vyas in Bengaluru Editing by Christian Radnedge)