The loss was the second straight for the Toreros (15-2, 4-2 West Coast Conference), who began the week undefeated and nationally ranked for the first time in program history. San Diego lost at Portland Wednesday.
Palmer scored 19 for the Zags (14-3, 4-1), who are nine-time defending WCC champs and who were ranked as high as 23rd earlier in the season.
Palmer and Keani Albanez each had four of GU's 12 steals as the Bulldogs forced 18 turnovers and held San Diego to less than 37 percent shooting, including 0-7 from 3-point range.
Malina Hood scored 13 for the Toreros. Sonja Greinacher added 14 for Gonzaga, Kiara Kudron 10.