Daiquan Walker's 3-pointer with 4:38 left cut UCF's deficit to 50-46. But neither team scored again until Johnson made two free throws with 36 seconds left. Johnson and Troy Caupain went 6 of 6 from the line in the final minute.
Octavius Ellis had eight points and 10 rebounds for Cincinnati (14-5, 5-2 American), which won its first conference road game of the season.
Kasey Wilson led UCF (9-10, 2-6) with 12 points and 11 rebounds. Walker finished with 11 points - with three of UCF's four 3-pointers - and Brandon Goodwin added 10. The Knights have lost four of their last five.