Gonzaga (10-2) closed the first half on a 15-4 run with Palmer scoring 11 to take a 36-28 lead.
Tia Pressley had 13 of her 19 in the first half for Washington State (6-6). Lia Galdeira added 15 for the Cougars, who had 24 turnovers
Palmer, who entered the game averaging 14.4 points after three-straight games of not reaching double figures, had 15 at halftime while the Bulldogs were grabbing 10 offensive rebounds and hounding WSU into 13 turnovers.
Lindsay Sherbert added 10 points for Gonzaga and Keani Albanez had 12, all in the second half. Danielle Walters had six assists after starting point guard Jazmine Redmon left early in the second half with an apparent concussion. Palmer also had six steals and three assists.