Since winning the Grand Prix de Saint-Cloud a year ago, Ange Gabriel has been superb, and the 5-year-old son of Kaldounevees gained sweet revenge on Sulamani for his defeat in the Dubai Sheema Classic in March.
"We were given an excellent lead and Thierry dosed the horse to perfection so he had plenty left at the end," Libaud told The Racing Post. "He gave him an economic ride."
Owner-breeder Antonia Devin said the ultimate goal for Ange Gabriel is the Arc de Triomphe.
Millstreet was taken down for coming off the rail and causing a chain reaction that stopped the charge of Ana Marie, who was moved to fifth.
Sulamani was four lengths behind the winner for Frankie Dettori and Godolphin racing manager Simon Crisford offered no excuse.
"Of course we're disappointed he didn't win," he said. "He was fit enough to win today and the firm ground was the same for the others.
"Let's reserve judgement on the horse until later in the season. We know he's top class and for some reason he didn't pick up in the straight."