Johnson, who finished with a career-high 27 points, slammed home a dunk with eight seconds left to seal the win for North Texas (5-8), which has won three of its last four games.
Johnson made 8 of 13 from the floor, including 3 of 6 from long range, and connected on 8 of 12 free throws. J-Mychal Reese added 13 points and Ja'Michael Brown chipped in 11. Jeremy Combs had eight points and grabbed 12 rebounds.
The North Texas defenders held the Bearkats scoreless for the final three minutes until Aurimas Majauskas, who had 17 points, nailed a trey with three seconds left.
Jamal Williams added 15 points for the Bearkats (5-8).