He outfoxed his rivals with a beautifully timed front-running ride on Aidan O’Brien’s four-year-old.
The jockey got the fractions spot on as the pair sped to a cosy success.
Only Frankie Dettori on Wings Of Desire put up any sort of challenge but was fought off easily.
The Queen’s Dartmouth never landed a serious blow although he stayed on late to grab third spot.
Moore said: “He’s a very good horse and has won in America and Hong Kong. It’s a marvellous achievement from Aidan to get him back in this shape to win this sort of race. He’s very professional.”
Horse racing: A Hong Kong obsession
Hugo Lascelles, racing manager to Wings Of Desire’s owner-breeder Lady Bamford, said: “Frankie thought he was going to get to Highland Reel but he just out-galloped him.”
John Warren, racing manager to Her Majesty, said: “The Queen is delighted. He is a genuine trustworthy horse that tries his best.”
Earlier, Fair Eva, a daughter of Frankel, was a brilliant winner of the Princess Margaret Stakes. She was cut to as low as 4-1 for the 1,000 Guineas next spring.