The four-year-old, who also won the King George VI and Queen Elizabeth Stakes at the same course in July, powered away in the final furlong.
John Gosden's Ombudsman had to settle for second place, with Almaqam holding off Delacroix for third.
Calandagan's success rounds off a remarkable flat-racing season for Graffard.
He also enjoyed his maiden Prix de l'Arc de Triomphe win with Daryz two weeks ago.
Earlier, there was a huge shock in the Champions Sprint as 200/1 shot Powerful Glory became the highest-priced winner of a Group One race in the UK.
Jamie Spencer moved the three-year-old into contention before edging favourite Lazzat in the final strides.
Odds-on favourite Trawlerman took the honours in the Long Distance Cup, while Kalpana eased to victory at 11/8 in the Fillies and Mares Stakes.
Cicero's Gift produced another massive surprise by winning the Queen Elizabeth II Stakes at 100/1.