Gonzaga limited the Tigers to 32 percent shooting from the field and then broke the game open late to set up a semifinals meeting with Oklahoma on Friday.
The Bulldogs (4-0) led by only two points with 8:30 to play after trailing by one at halftime.
Elias Harris added 13 points and nine rebounds for Gonzaga, which made 47 percent of its shots.
Adonis Filer was the only player in double figures for the Tigers with 10 points. Clemson had won its opening two games of the season.