Goalkeeper Maddie Hinch was the heroine for Britain on Friday, making numerous key saves in the match before keeping a clean-sheet in the shoot-out as she played a starring role to help her team achieve a moment of sporting history.
The result ended the Dutch quest for a third successive Olympic gold medal, following their victories at the Beijing 2008 and London 2012 Olympic Games.
Hinch provided early evidence of the pivotal role she would play by saving a penalty stroke from legendary Netherlands captain Maartje Paumen before Lily Owsley gave world No.7 Britain a first quarter lead.
World No.1 the Netherlands were almost totally dominant in the second period, levelling the scores within a minute of the restart when 2015 FIH Player of the Year Lidewij Welten supplied Kitty van Male who made no mistake with a sensational backhand strike into the roof of the net.
Although Hinch continued to deny the Dutch at regular intervals and Naomi van As rattled the cross-bar, the Dutch eventually netted again when drag-flick expert Paumen producing a rare strike from a penalty corner to give her team a 2-1 lead.
Remarkably, Britain hit back almost immediately when Crista Cullen slapped home from open play just before half time.
But the Dutch continued to control the game in the third quarter, launching wave after wave of high paced attacks before making it 3-2 thanks to Van Male's second of the game.
The Netherlands continued to dominate in the fourth and final quarter, but it was the gritty Brits who tied the scores when Nicola White bundled home a penalty corner to take the match into a shoot-out where Britain shot-stopper Hinch came into her own.
Hinch, who also starred in last year's shoot-out victory over the Netherlands in the final of the Unibet EuroHockey Championships in London, made saves from Willemijn Bos, Ellen Hoog and Laurien Leurink before Margot van Geffen crashed her effort against the post with Britain leading 1-0.
Margot van Geffen's miss meant that if Holly Webb scored, Britain would be the Olympic champions for the first time in their history. Webb made no mistake, keeping a cool head to fire past Netherlands goalkeeper Joyce Sombroek to give Britain an incredible victory against all the odds.
In the bronze medal match, world No.9 Germany were forced to soak up huge amounts of pressure from world No.9 New Zealand for most of the first two periods and into the early stages of the third before taking a shock lead in the 34th minute.
Charlotte Stapenhorst, 21, was the scorer, forcing home from close range after a brilliant passing move ripped open the Black Sticks back-line.
Die Danas added to their lead four minutes later with another fine attack, with Lisa Sch?tze showing the killer instinct in front of goal that the dominant New Zealanders appeared to be sadly lacking.
Olivia Merry pulled the New Zealanders back into it when she forced home a penalty corner resulting in even more sustained pressure on the Germany backline.
But a virtually flawless defensive performance ensured that the Europeans claimed their first Olympic medal since winning gold at Athens 2004. It was a painful defeat for New Zealand, who lost the bronze medal match for the second Games in succession.
