Moore completed 21-of-33 passes for 278 yards with two touchdowns passing, and his 1-yard scoring run led to a 24-7 halftime lead.
The third scoring pass made Boise State's lead 31-7 with 10:22 left in the third.
Doug Martin gained 63 yards on six carries with one touchdown.
Austin Pettis scored once on five receptions for 63 yards, and Mitch Burroughs caught a scoring pass for the Broncos (8-0, 3-0 Western Athletic Conference), who were one of five unbeaten teams after their 26th straight home victory.
San Jose State's lone touchdown came on Jordan La Secla's 11-yard pass to Marquis Avery with 11:28 left in the second.
La Secla went 11-for-20 for the Spartans (1-6, 0-3), who sank to 0-10 all-time against the Broncos.