Carr connected on 37-of-48 passes for 419 yards as the Bulldogs posted their first 5-0 start since 2001.
Adams finished with 16 catches for 185 yards.
Marteze Waller rushed for 157 yards and two scores on 19 carries for Fresno State.
The Vandals (1-5) were led by Chad Chalich, who made good on 14-of-32 passes for 100 yards, one touchdown and three interceptions.
Backup Joshua McCain went 3-of-8 through the air for 77 yards, one touchdown and an interception for Idaho.