The Canadian pair were trailing 0.23sec after Tuesday's first two runs, but produced two more consistent bursts to clock a combined time of 3min 50.61sec finishing 0.1sec ahead of the second-placed USA-1 team.
Williams, a silver medallist at the 2004 Athens Olympics and part of the 2012 gold-medal relay squad in London, was the brakewoman on USA-1, piloted by Elana Meyers.
She is the first woman and only the second person in history to win medals in Summer and Winter Games.
USA's Eddie Eagan won a boxing medal at the 1920 Summer Games and a four-man bobsleigh medal at the 1932 Olympics.
Meyers and Williams, who led by 0.23sec after first two runs on Tuesday, made errors on Wednesday which forced them into the silver medal position.
The USA-2 team of Jamie Greubel and Aja Evans won bronze with a time of 3min 51.61sec.
The third US team of Jazmine Fenlator and former US Olympic hurdler Lolo Jones, who was a controversial selection with some critics claiming she had been selected for her good looks and high media profile, were 11th.
