It was Washington State's first road victory over Washington since a 75-72 overtime game in 1993 and their first sweep of the Huskies since 1975.
The victory earned Washington State its best conference start in program history, going undefeated in its first four Pac-12 games.
Shalie Dheensaw recorded her second straight double-double with 20 points and 13 rebounds for Washington State (10-6, 4-0 Pac-12).
Freshman Kelsey Plum scored a career-high 30 points for Washington (8-7, 1-3). Jazmine Davis added 22 points and Aminah Williams pulled down 15 rebounds.
The final score doesn't reflect the close contest that it was for much of the game with 12 lead changes and 13 ties.
Dheensaw and Mariah Cook combined for seven consecutive points to give Washington State a 57-49 lead early in the second half.
Plum's 3-pointer tied it at 65 with 7:29 remaining and her basket on the next trip down the floor gave the Huskies their first lead of the second half with 6:31 left.
The game was tied four times in the final 6 minutes.
The Huskies were never able to push its lead past two points, and Sage Romberg's 3-pointer at the 2:19 mark gave Washington State a 76-73 lead.
Galdeira gave the Cougars a five-point lead three times in the final 2 minutes in the back-and-forth affair. She scored seven of the Cougars' final nine points of the game.
The Cougars defense only allowed two Washington field goals in the final 4 minutes.
Washington State jumped ahead 13-3 in the games' opening minutes. Washington responded and Plum's basket gave the Huskies their biggest lead of the half at three points, 19-16. The Huskies led by three again with 2:37 left, but Presley scored the next nine WSU points and the Cougars led 42-40 at the break.
There were eight lead changes and seven ties in the opening 20 minutes.
Washington center Katie Collier suffered a head injury Tuesday and only played 6 minutes in the first half, four in the second. Davis had 16 points in the opening 20 minutes and Plum had 13 on 5-of-13 shooting for the Huskies. Williams had eight rebounds, seven on the offensive glass.
Earlier in the week, Washington State ended a 36-game losing streak to the Huskies.
The Cougars fell to Washington last year in Seattle, 60-53.