Johnson, who had 21 carries, crashed over from 2 yards out with 3:29 to play to put Miami (2-0) ahead 21-9 and give the Hurricanes the cushion they needed to withstand Solomon Patton's touchdown catch on Florida's (1-1) next possession.
Florida got the ball back on an onside kick with 28 seconds to play, but the Miami defense sacked quarterback Jeff Driskel on the first play of the series.
Driskel completed 22-of-33 passes for 291 yards and was intercepted twice. Florida lost three fumbles and was penalized 10 times for 69 yards compared to five flags for 58 yards for Miami.
Miami's Stephen Morris was 12-of-25 for 162 yards, two touchdowns and one interception. Herb Waters caught one of the scoring tosses and Phillip Dorsett hauled in a 52-yard TD pass late in the first quarter.