Galdeira was 7 of 15 from the floor for the eighth-seeded Cougars (11-19), who moved on to face No. 1 seed and fourth-ranked Stanford on Friday.
Janae Fulcher led the No. 9 seed Sun Devils (13-18) with 20 points, her third 20-point game of the season and second against Washington State. Promise Amukamara grabbed 14 rebounds but was just 1 of 12 shooting, part of a 29 percent team effort for ASU.
The Sun Devils led 18-13 at halftime, but the Cougars rallied in the second half, going ahead for good, 29-27, on Sage Romberg's jumper with 14:58 left and building on the lead from there.
Washington State coach June Daugherty missed the game her first absence in her 24-year coaching career with acute appendicitis. The school said Daugherty had surgery Thursday evening and was expected to be discharged Friday morning.
Daugherty's husband, assistant coach Mike Daugherty, filled in. He said his wife was "doing well" and was hopeful that she'd be released from the hospital in time to coach against Stanford on Friday.
"I hope so, because I want to retire 1-0," Daugherty said. "I'd like to go out undefeated."
After ASU dominated the first half, WSU returned the favor in the second after a halftime pep talk from the Cougars' interim coach.
"We told them at halftime, 'We're playing great defense. The toughest team is going to win this game. If you guys just stay with it, the ball will start going in,'" Daugherty said. "Pretty much all of that came true."
ASU coach Charli Turner Thorne was on the wrong end of the second-half turnaround and was disappointed afterward.
"We played a good 20 minutes, then we faded," she said. "It's disappointing, but just lessons learned. We're a very young team and looking forward to coming back next year with a roster at full strength."