Johnson recorded five steals as Tigers (10-2, 1-0 AAC) notched a third straight win overall in kicking off their American Athletic Conference schedule.
Joe Jackson added 18 points with five rebounds.
Michael Dixon contributed 18 points and five assists for Memphis, which took control with a 13-2 run midway through the first half.
The Bulls (9-5, 0-1) were led by John Egbunu with 20 points and 14 rebounds.
Victor Rudd had 17 points and nine boards.