8 Gonzaga escaped with a 75-74 victory against BYU in a West Coast Conference game Thursday night in Provo, Utah.
Johnson scored 18 points for the Cougars (13-7, 3-2) and Gideon George and Jaxson Robinson added 17 apiece.
Adem Bona added 15 points on 7-of-9 shooting and collected eight rebounds for the Bruins (15-2, 6-0 Pac-12), who won their 12th consecutive contest.
Jaylen Clark added 11 points, five rebounds and three steals, and Jaime Jaquez Jr. had eight points, 12 rebounds and six assists for UCLA.
Rollie Worster scored 12 points to pace the Utes (12-6, 5-2), who lost their second straight game.