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.
FOX Sports' Bruce Feldman joins The Paul Finebaum Show to share his thoughts on the upcoming National Championship race.
Urban Meyer, Thad Matta and Ohio State athletic director Gene Smith were among the crowd at the parade for the Cleveland Cavliers on Wednesday.
Cal has many holes to fill on defense after losing six of their seven leading tacklers from last season.
New Mexico, like most teams, had a hard time getting Emmitt Smith on the ground.
Auburn coach Gus Malzahn could use a signature win as much as any coach in the SEC, and beating a title contender like Clemson would certainly qualify.
Safety Fish Smithson's leadership and playmaking ability should make him the foundation of Kansas' defense.