The Wildcats (22-5, 11-4) trailed 58-46 with 7:42 remaining in regulation before using a 12-2 spurt to close the gap.
They took a 67-65 lead on a Lisa Griffith's 3-pointer with 30 seconds left.
Oregon State (14-14, 10-6) forced overtime when Chassie Wiersma made two free throws with 1.7 seconds left.
But Arizona never trailed in the extra period as Tatum Brown and Reshea Bristol had four points apiece.
Oregon State's attempt to force double overtime failed as Felicia Ragland's last-second shot hit the rim and bounced off.
Elizabeth Pickney paced the Wildcats with 17 points. Bristol added 15 while Brown had 14 and Angela Lackey 13 for Arizona, which set a school record by making 20 of 22 free throws in the game.
Sissel Pierce scored 19 points for the Beavers, who led by 13 in the first half and 36-34 at halftime. Ragland and Reda Petraitis each finished with 16 points.