Tia Presley added 13 points and the Cougars (9-6, 3-0 Pacific-12 Conference) moved into a first-place tie with USC.
Jazmine Davis led Washington (8-6, 1-2) with 27 points and nine rebounds. Davis scored 20 points after WSU built a 42-31 halftime lead.
The lead changed hands throughout the second half. Galdeira scored WSU's final two points at the free-throw line with 15.5 seconds remaining. Washington's Talia Walton put-back a rebound with 5 seconds to go. After Presley missed a free throw, Washington's Chantel Osahor saw her desperation shot from beyond midcourt bounce off the glass as time expired.
The Cougars, who have not had a winning season since 1995-96, had not defeated Washington since winning 72-67 on Feb. 25, 1995, in Pullman.