Felicia Ragland added 12 points and eight rebounds as the Beavers (15-11, 7-9 Pac-10) snapped an eight-game losing streak to the Wildcats (18-9, 8-7).
Elizabeth Pickney led Arizona with 24 points and 10 rebounds.
With the game tied, Hollye Holbrook made one of two free throws to give the Beavers a 64-63 lead with 1:05 to play.
Arizona had a chance to take the lead with 20 seconds left, but Syesha Thomas stole the ball from Reshea Bristol.
Veranda James was called for an intentional foul and Thomas made both free throws with 10 seconds on the clock.
Oregon State inbounded and Cook was sent to the free-throw line, where she made the first half of a one-and-one and gave the Beavers a 67-63 lead with eight seconds left.
Bristol hit a 3-pointer as time ran out to finish the scoring.
Bristol finished with 19 points, nine assists and seven rebounds but also had 11 turnovers.