Kevin Foster had 13 points and Allen Huddleston 11 for the Bulldogs (8-13, 2-6 Mountain West), who took control of the game with a 19-6 run over an 8:30 stretch of the second half.
Anthony Marshall scored 19 points and Anthony Bennett 15 for the Runnin' Rebels (17-6, 4-4).
Johnson sparked Fresno State's decisive run, scoring 10 points. His jumper culminated the surge, giving the Bulldogs a 51-36 cushion with 6:20 remaining.
Braeden Anderson made his debut for Fresno State, going 0 for 2 from the floor with two rebounds in 12 minutes. The 6-foot-9 freshman came to Fresno State after failing to gain Big 12 approval as a partial qualifier at Kansas in 2011 and had to sit out the first 20 games of this season due to NCAA transfer rules.
The Bulldogs snapped a four-game losing streak.