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.
Western Kentucky commit Jared Nash launches this snap from the bleachers and successfully sinks it in the garbage can.
Florida State coach Jimbo Fisher hopes quarterback Sean Maguire is ready to go full speed by the middle of June.
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After transferring in from Montana State, Dakota Prukop has a checklist he's working from as he prepares to compete for the Oregon job.