Johnson completed just 4 of 11 passes for 43 yards, but added 75 yards rushing on 16 carries and his 32-yard touchdown pass to Warren Redix with 7:51 left proved to be the winner.
Trevor Moore's 28-yard field goal with 2:18 left in the first quarter opened the scoring and North Texas (1-11, 1-7 Conference USA) took a 3-0 lead into halftime.
Johnson scored on a 5-yard run early in the third but UTEP (5-7, 3-5) missed the PAT and led 6-3.
North Texas sandwiched Tre Johnson's 53-yards punt return for a score and Cortney Finney's 13-yard fumble return for a touchdown around Smith's pick-6 to take a 17-13 lead into the fourth.
The teams combined for 461 total yards and seven turnovers.