The Wolf Pack (8-7, 1-1 Western Athletic Conference) rallied to force overtime in the final 15 seconds.
Babbitt made one free throw and his missed second foul shot was rebounded by teammate Lyndale Burleson and Malik Cook's tip-in with 12 seconds left tied the score at 67.
Babbitt's two free throws with 2:18 remainig in overtime put Nevada ahead to stay at 71-69.
Johnson hit a jumper with 1:44 left and he made two foul shots with 37 seconds showing for a 75-69 lead.
Two free throws apiece by Babbitt and Johnson capped the Wolf Pack's 10-0 run for a 79-69 bulge with 13 seconds left.
Babbitt's 22 points tied his career high and he added 12 rebounds. Joe Shaw finished with 13 points for Nevada.