The Roadrunners held off Troy down the stretch by making six straight free throws in the final 22 seconds. There were seven ties and eight lead changes before UTSA took the lead for good at 54-53 on a layup by Alex Vouyoukas with 9:40 to play.
Vouyoukas added 13 points and Jeromie Hill had 13 rebounds for the Roadrunners (6-5), who outscored Troy 28-4 in the paint.
Johnson, who made 9 of 12 field goal attempts, helped the Roadrunners shoot 52 percent (26 of 50) from the field.
Troy, which averages 10 3-pointers a game, made 16 from long range but shot only 39 percent (23 of 59 from the field).
Will Weathers scored 23 points and Alan Jones added 21 for the Trojans (5-6), who have lost three of their past four games.