The Bulldogs improved to 9-0 and are one of the 18 unbeaten teams left in major college basketball.
There were 20 such teams when Wednesday's action began, but Colorado State and Stephen F. Austin both suffered their first setback. Florida, Charlotte, New Mexico and Temple also stayed unbeaten Wednesday.
Gonzaga had a one-point lead when Gary Bell was fouled with 14 seconds to play. He could make only 1-of-2 from the line and DaVonte Lacy tied it for the Cougars by hitting a layup with 7 seconds to go.
That set the stage for the winning shot by Pangos, who made only 2-of-11 from the field while scoring eight points.
Elias Harris led Gonzaga with 23 points and Kelly Olynyk had 22. Washington State (5-4) was paced by Brock Motum with 23.
Gonzaga overcame a four-point halftime deficit and built as much as a seven-point advantage with less than 8 minutes left in the game.