The Golden Eagles (7-1, 3-1 Conference USA), who won their sixth straight game and are knocking on the door of a Top 25 ranking, broke open a 10-10 game in the second half when Davis threw scoring passes of 47 yards to Quentin Pierce and 15 yards to Dominique Sullivan, and Woodyard scored on a 68-yard run.
Davis also had a 1-yard TD pass to Ryan Balentine in the first quarter and finished with 190 yards passing.
UTEP (4-4, 1-3), which was held to 262 yards of offense, got its only touchdown in the first quarter on a 1-yard run by Leilyon Myers. Dakota Warren added a pair of field goals for the Miners.
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UCLA junior linebacker Myles Jack has withdrawn from school and will enter the NFL draft, making the decision just weeks after suffering a season-ending knee injury.
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.
Auburn senior receiver D'haquille Williams has been dismissed from the team.
Alabama coach Nick Saban took exception with the media's outlook on his team prior to Saturday's win at Georgia, lashing out at those who "buried" the Crimson Tide.
DraftKings and FanDuel continued to defend their integrity after the disclosure that a DraftKings employee won $350,000 with information used in a way that some have likened to insider trading.