Black grabbed seven rebounds while Johnson chipped in with six boards and five assists for Memphis (1-0), which is coming off a second-round exit in last year's NCAA Tournament.
Antonio Barton supplied 11 points off the bench in the victory.
The Ospreys (1-1) were led by Jerron Granberry with 14 points and Parker Smith with 12.
Teacher apologizes for showing sexual image of herself in class
Jessica Simpson shares three-way kiss with friends in photo