Minutes after their men had won gold in their final, the Dutch looked set to add a second but after a titanic struggle the British foursome pulled themselves across the line with one last big effort to win by 0.15 seconds, with Germany third.
The Netherlands crew appeared to have comfortably dealt with the British challenge from the midway point of the race, but Britain's crew somehow found the energy to mount a last desperate challenge to stun the Dutch at the finish line.
"We got to 250 (metres) to go and I could sense we were coming back, so I was like, 'Guys, now, we're going now'," Britain's Lauren Henry said. "And then I called it again about 150 metres to go, I was like, 'We can do this.'"
"I kind of knew we'd crossed the line first but we had to wait to see, and when I saw 'GBR, 1' come up it was amazing."
The Dutch did, however, retain their Olympic title in the men's quadruple sculls with a tremendous display of power and control, with Italy second and Poland third.
The Netherlands' crew took an early lead but were quickly reined in by the rest of the field before edging in front again with the Italian, Polish and British crews close behind.
The Dutch rowed smoothly to open up a lead of just over half a length that they never relinquished and they won with a time of 5:42, 2.4 seconds ahead of Italy.
"We knew it was good, but we knew we had to stay sharp and step up the game a bit," Dutch crew-member Tone Wieten said.
"The last few days were challenging, especially when you get fitter and fitter, to stay together, but in the end, the moment that counts, we did it. It's amazing."
Italy engaged in a mid-race battle with the British crew, emerging victorious and then passing the Poles to grab second spot by 0.19 seconds, with Britain ending an agonising fourth.
