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.
South Carolina AD Ray Tanner is not "100 percent sure" Saturday's game vs. No. 7 LSU will be played at Williams-Brice Stadium because of devastating floods that hit the state.
UCLA junior linebacker Myles Jack has withdrawn from school and will enter the NFL draft, making the decision just weeks after suffering a season-ending knee injury.
The Oklahoma State Cowboys' defense has lost senior middle linebacker Ryan Simmons for the season because of a knee injury.
A judge has dismissed simple assault charges against Rutgers wide receiver Leonte Carroo after the woman he allegedly attacked after a football game said she didn't want to testify.
Colorado coach Mike MacIntyre said he was sorry for getting into a sideline altercation with an assistant coach during a 41-24 loss to Oregon over the weekend.
The Fresno County District Attorney's office has filed charges against Fresno State quarterback Zack Greenlee and a teammate arrested last month during a house party near the campus.