Cole Huff had 11 points and Ali Fall 10 for the Wolf Pack (2-1).
Jackson Stevenett's two free throws got Southern Utah within a point, 55-54, with 8:37 remaining. But Burton made six free throws and Story scored 14 points, including three 3-point shots, to ignite a 20-4 Nevada run.
The Thunderbirds went scoreless for a 3:30 stretch. Story culminated the surge with a layup that made the score 75-58 with 2:29 to play.