Louie Sakoda connected on field goals of 43 yards and 38 yards for the Mountain West Conference-leading Utes (9-0, 5-0).
Johnson was 23-of-32 for 195 yards and one interception. Matt Asiata picked up 80 yards rushing on 12 carries.
Brad Gruner was 16-of-25 for 170 yards, and also rushed 57 yards for the Lobos (4-6, 2-4), who have lost two straight.
Rodney Ferguson scored on a 10-yard run for New Mexico in the third quarter to get the Lobos within a field goal, but New Mexico was unable to get any traction after that.
James Aho kicked a 38-yard field goal for the Lobos.