Sir Michael Stoute's horse put up a career-best effort following on from his seasonal reappearance third in the Earl Of Sefton Stakes at Newmarket.
Always prominent just off the pace set by Ostilio and Laurens, Jim Crowley switched the winner to the outside of the runner-up inside the final two furlongs.
Mustashry responded well to pressure and ran away from the field inside the final furlong, the 9/1 shot winning by two-and-a-half lengths as Laurens held off Accidental Agent for second with Romamised running on for fourth.
Stoute said: "We knew this horse was in very good shape and I have to confess that it's Jade (Ransley) who has made this horse - she rides him and has looked after him from the very start.
"He's had his niggles, but I've never had him better than today.
"The Queen Anne is the race that comes to my mind, while remembering he is versatile and has won over a mile and a quarter.
"But I think the Queen Anne is what Sheikh Hamdan wants."
Crowley said: "He beat a good filly into second, and he now feels like a proper horse, having won over seven, a mile and a mile and a quarter.
"He had a little blip at the Breeders' Cup, but he's won well today."
Karl Burke is eyeing a rematch with the winner at Royal Ascot for Laurens.
The North Yorkshire trainer said: "I was delighted with her run, she lost her lead, but then in the last 50 yards got her second wind and stayed on again, so I'm sure there's some improvement in her.
"She will go for the Queen Anne next and it will be fillies' only (races) after that."
