The American duo in USA 2 pulled off the historic win by staving off tough competition from the two powerful German teams.
Germany 1's Sandra Prokoff and Ulrike Holzner had to settle for silver, while Germany 2's Susi-Lisa Erdmann and Nicole Herschmann grabbed bronze.
Further back, Britain's Michelle Coy and Jackie Davies in GB 2 finished 11th, in front of 12th placed Cheryl Done and Nicola Gautier in GB 1.
But it was a fairy-tale story for Bakken and Vonetta, who had started the competition as underdogs to the other American bob driven by 2000 and 2001 World Cup champion Jean Racine.
But it was clear that USA 2's pair had not read the form book.
Upsetting the favourites
Bakken, aided by brakewoman Flowers, set the fastest time in the competition on their first run to go straight into the lead.
They then set the second fastest time of the day to win in a combined time of one minute and 37.76 seconds to the obvious delight of the home crowd.
Germany I and 2, who were among the pre-race favourites, finished 0.30 and 0.53 behind USA 2.
Germany 1's pair looked as though they might threaten the Americans after setting the fastest push time of 5.29 seconds on their second run.
But US 2 had done enough on the lower part of the track to claim victory. and America's first gold medal in the Olympic bobsleigh since 1954.
USA 1, driven by Racine, finished a disappointing fifth, one behind Switzerland's Francoise Burdet, who took the two-woman gold at last year's World Championships in Calgary.