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.

The study, by Carnegie UK Trust, showed 51% of people aged 15-24 used libraries in 2016 - an increase of 9% since 2011.
Overall, there has been an increase in public library use, from 45% to 46% over five years.
Northern Ireland has also seen its library use go up, but there have been declines in England and Scotland, the wellbeing trust said.
The findings are based on 10,000 interviews conducted in 2011 and 2016.
The trust said there was also a jump in library use in households with pre-school children (7%) and primary age children (3%).
Chief executive Martyn Evans said: "Public libraries remain an immensely popular civic resource, both in Wales and across the rest of the UK and it's extremely promising that there's been a rise in library use in Wales amongst households with pre-school and primary children, as well as young people."
Harry Angel won the prestigious July Cup in brilliant style over six furlongs at Newmarket.
[NEXT_CONCEPT]
More than half of young people in Wales use public libraries, research has shown.