The three-year-old, ridden by Adam Kirby and trained by Clive Cox, is part of Sheikh Mohammed's Godolphin team.
Last year's winner Limato was second, a length and a quarter behind, with Brando in third.
Aiden O'Brien's Caravaggio, a heavy favourite who beat Harry Angel in June's Commonwealth Cup at Royal Ascot, finished fourth.
Harry Angel made a solid start and tracked Caravaggio's pacemaker Intelligence Cross in the early parts of the race before taking the lead in the final furlongs.
Caravaggio, ridden by Ryan Moore, went into the race unbeaten with six wins out six but never looked like bridging the gap, as Harry Angel won by an impressive length and a quarter from Limato.
"He's always been special. We always hoped he'd be Group One material and he is," said trainer Cox.
"It's great to get a winner for Sheikh Mohammed on his birthday. Today I was very confident about his whole demeanour, it's just a joy to be involved with top-flight horses."
Jockey Kirby added: "He's the best. He's gone from a boy to a man with every race he's had."
Cornelius Lysaght, BBC horse racing correspondent
The first major contest between the three-year-olds and the older horses - in the Eclipse Stakes a week ago - went narrowly to the seniors. This result boosted the younger lot emphatically. In this division, they're pretty good.
Clive Cox was convinced Harry Angel had not just come out well following his defeat by Caravaggio at Royal Ascot in June, but that he had flourished since, and that's what was demonstrated.
Continuing a fine year for the Godolphin string, Harry Angel, bought by Sheikh Mohammed before Ascot, swept aside his rivals, with Caravaggio - part of the operation of Coolmore, Godolphin's arch rival - only fourth here.
Harry Angel won the prestigious July Cup in brilliant style over six furlongs at Newmarket.