All the talk before race centred around the last year's stunning Prix de l'Arc de Triomphe winner but the four-year-old Treve struggled to maintain touch with early leader Elkaayed.
The Fugue patiently bided her time in second but once she found her stride, neither Elkaayed or Treve could keep up.
"She's been an absolute star for me and everybody back at the yard," Buick was quoted as saying on the BBC. "She proved today what she can do against top-class horses.
"When she gets an uncomplicated run like she did today and they come back to her, she's lethal, like she was there. It means everything to everyone involved."
The Fugue crossed the line in a new course record to become trainer Gosden's second Group 1 winner in as many days.
Frankie Dettori, Treve's rider, said he was worried about her performance from the early stages.
"Going to the start she didn't feel like Treve and at the back of my mind I knew then I was in trouble," he said.
"I was hoping in the race she would loosen up and warm up, but I knew my fate at the three-furlong marker. She ran a good third, but it's not the Treve we all know.
"Something is definitely wrong and what's wrong was before the race."
Earlier in the day Mustajeed, ridden by jockey Pat Smullen, won the Jersey Stakes before Anthem Alexander held on to take victory in the Queen Mary Stakes.
(Reporting By Tom Hayward, editing by Pritha Sarkar)
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