Williamson's game-winning boot came after Oregon's Alejandro Maldonado missed a 41-yard field goal try in the first possession of the overtime.
The Cardinal (9-2, 7-1 Pac-12) forced overtime when Kevin Hogan hooked up with Zach Ertz on a 10-yard scoring pass with 1:35 left in regulation.
Ertz had initially been deemed to be out of bounds when he made the catch, but a video review overturned the ruling on the field.
With the loss, Oregon fell to 10-1 and 7-1 in the Pac-12, likely falling out of the top two spots in the Bowl Championship Series rankings thanks to Notre Dame's rout of Wake Forest and Alabama's thumping of West Carolina.
The Ducks could have also seen their shot at the Rose Bowl evaporate since Stanford owns the tiebreaker over them in the Pac-12 North.