The victory - his first in a Group One race - made amends for an unlucky showing at Goodwood's Richmond Stakes in July, which saw Perfect Power finish fifth of seven runners.
His one-and-a-quarter length victory over Trident in France was a strong return to form after he had won the Norfolk Stakes at Royal Ascot in June.
He'll now move on to the Middle Park Stakes at Newmarket, which will run on September 25.
Bruce Raymond, racing manager to owner Sheikh Rashid Dalmook Al Maktoum, said: "He looks like being a decent horse. Any horse that quickens like that has got a huge advantage over anything else.
"I think he was a bit unlucky in the Richmond. They didn't go much pace, and poor Paul (Hanagan) couldn't get anywhere. He got stopped wherever he went - and then the race was over.
"I expected him to beat all those that ran in the Richmond. It was good.
"It will be the Middle Park next, and then we'll see about next year."