The Hornets (2-3, 1-0 Big Sky) jumped ahead late in the second quarter as Safron threw a 15-yard touchdown to Carter with just over a minute remaining, then recovered a punt at the 15 and Safron found Carter again to take a 14-0 halftime lead.
Sacramento State pulled away in the third quarter as Safron connected with Chris Broadnax for a 16-yard touchdown.
The Wildcats (1-4, 0-1) responded with a field goal, but Safron answered, hitting Carter with a 51-yard scoring strike.
Safron was 25-of-31 with 288 yards and an interception and Carter finished with eight catches for 148 yards.
The victory was the Hornets' first in Ogden as they had loss their previous eight games at Weber State.