Gloyd, who led five players in double figures, also had a team-high eight rebounds.
Davellyn Whyte had 12 points and 11 assists for the Wildcats (9-3). Kama Griffitts had 14 points, Cheshi Poston had 12 and Erica Barnes added 10.
Washington State led 34-31 at halftime, but Arizona's offense kicked in during the second half, shooting almost 52 percent. Arizona shot 44.8 percent from the field for the game, while Washington shot 33 percent.
Arizona hit all nine of its free throw attempts in the final 60 seconds.
Lia Galdeira scored 17 points to lead Washington State (4-8). Carly Noyes had 14 points and nine rebounds, including the 400th of her career. Sage Romberg added 10 points.
The Cougars hit a season-high eight 3-pointers.