The Broncos remained unbeaten in five games, setting up their inaugural Mountain West Conference encounter next week at Colorado State.
Moore completed 23-of-31 passes for 254 yards and sat out the fourth quarter. He has completed 71.5 percent of his throws through five contests with 14 touchdowns and four interceptions.
Moore opened the scoring with a 4-yard throw to Matt Miller on Boise State's opening possession, and then hit Geraldo Boldewijn with a pair of touchdown throws in the second period for 18 and 4 yards.
The third TD pass came with 20 seconds left in the first half and gave Boise State a 37-0 lead at intermission.
Harper's scored from 6 yards in the second period and ran 3 yards for a TD in the third. Doug Martin led the Broncos on the ground with 94 yards on 16 carries.
Fresno State (2-4) fell behind 50-0 before Devon Wylie scored on a 79-yard punt return 16 seconds into the final period.
Boise State defeated Fresno State 51-0 last year when both teams were part of the Western Athletic Conference.
Celebrity Breakups and divorces of 2014 [PHOTOS]