The two teams were tied on eight penalty points after the team competition, sending the event into a shoot-out over a shortened course.
And while two Dutch riders faltered, Nick Skelton, Ben Maher and Peter Charles all went clear to snatch gold.
Overnight leaders Saudi Arabia took the bronze with a score of 14 points.
It was Britain's first Olympic showjumping medal since 1984 and their first gold since the Helsinki 1952 Games"