The 10/11 favourite hit the front late in the two-and-a-half mile race and beat Mizzou into second by three lengths, with Sheikhzayedroad third.
Order Of St George’s fifth successive win took Moore’s tally of victories at the meeting to 39, though he was quick to praise O’Brien, who has now saddled 51 Royal Ascot winners.
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“All the superlatives have been said about Aidan,” he said. “This win has just endorsed what everyone knows and says: he is one of the great trainers.”
Moore had to bide his time in the feature race on Ladies’ Day, with Mille Et Mille setting the early pace and opening up an early 10-length lead.
“I had to ride about four different races – it was a nightmare,” he added. “He picked up very well and after two and a half miles, he was pouring it on at the end. He’s a class horse and class horses win races.”
Moore and O’Brien had already teamed up earlier to win the Ribblesdale Stakes with 15/8 favourite Even Song.
The Queen’s horse Guy Hawkes, meanwhile, was put down after suffering a broken leg in the day’s final race, the King George V Stakes, in which William Twiston-Davies rode Primitivo to victory.