The teams were tied on eight penalties after each of their four riders had jumped in the final and were put through their paces once more in the equestrian equivalent of a penalty shoot-out to decide the medals.
Brits Nick Skelton, Ben Maher and - in a dramatic final ride - Peter Charles jumped clear rounds in the showdown to clinch the gold - to add to Team GB’s eventing silver.
Jur Vrieling cleared in reply but Maikel van der Vleuten collected eight penalties and Marc Houtzager another four, leaving the Dutch with 12 points to Britain’s zero.
The worst scoring run from GB's Scott Brash, who picked up four penalties, was discounted while Gerco Schroder did not start as Great Britain’s clear rounds could not be bettered.
Saudi Arabia claimed an excellent bronze, as their investment in horses was finally matched by skill in the saddle. They had never won a team medal before, with an individual bronze from Sydney the only Olympic trophy for the horse-breeding nation.
The victory is particularly special for life-long jumper Skelton, 54, who almost retired in 2000 after breaking his neck. It was also vindication for the selection of Charles, who was widely criticised but executed a perfect final round before punching the air with his fist in celebration.
"It has taken me 54 years," said Skelton, who first rode as an 18-month old toddler. "It is unbelievable and what a place to do it. I have got a wonderful horse (Big Star) and it is a dream come true.
"It is great for our country and great for our sport. The lads have done great. I’m really pleased for Pete [Charles]. He has had a rough trip but he came good in the end."
In the final itself, Skelton had jumped his third clear run of the competition on Big Star, and Brash on Hello Sanctos also produced a faultless performance to consolidate his earlier eight penalty points.
Maher on Tripple X III picked up four jumping penalties – his first of the competition – while Charles collected five on Vindicat to help minimize their overall total and see them into the jump-off.
The medal comes as an Olympic first for all four team members and Great Britain’s first since silver in Los Angeles in 1984, while bronze was awarded to overnight leaders Saudi Arabia on 14 points.
Skelton, Maher and Brash will also progress to Wednesday’s individual jumping medal rounds but Peter Charles was eliminated in the first round.