The three-year-old filly went off the 1-5 favourite and won by a length and a quarter to add to her previous victories this season in the 1,000 Guineas and the Oaks.
Minding's win was a third in the race for trainer Aidan O'Brien and seventh of the meeting for jockey Moore.
Queen's Trust (16-1) finished second, with 14-1 chance Jemayel third.
Minding was last of the five runners turning into the home straight but, after being shaken up by Moore, got to the front with a furlong to go and eased clear.
Moore, the meeting's leading jockey, said: "She's got an awful lot of class and was only doing what she had to do.
"It's a hard campaign she's had. She's a very special filly."
Later on the card, the Stewards' Cup was won by 9-2 favourite Dancing Star, ridden to land a significant gamble by David Probert and trained by Andrew Balding.
BBC horse racing correspondent Cornelius Lysaght
"Minding wasn't at her most impressive here, probably because of the good to firm going, but she was never going to be caught late on by runner-up Queen's Trust, who ran a tremendous race.
"The question now is when will this champion female take on the guys?
"Listening to her trainer afterwards it sounded that a likely aim is October's Prix de l'Arc de Triomphe when, as a three-year-old and a filly, she has the advantage of the least weight.
"Dancing Star looked truly a chip off the old block as she emulated her grandmother Lochangel's half-sister Lochsong, one of the race's most celebrated winners. And how nice she did it in the same silks, those of owner/breeder Jeff Smith.
"True, the 3-year-old had the best of the draw, which allowed her easy access to race on the favoured 'far-side', but she demonstrated real authority.
"Lochsong, who was four when she won, went on to be champion sprinter twice, so will Dancing Star copy her in that respect too? She's improving all the time and it's most certainly possible."
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Minding, ridden by Ryan Moore, won the Nassau Stakes at Glorious Goodwood to claim a sixth Group One victory.