Austin Pettis hauled down one of Moore's touchdown strikes and also passed for a score for the Broncos (3-0), who notched their 17th straight overall victory.
Moore ended the night 19-of-27 passing for 288 yards. Five receptions went to Titus Young for 136 yards and a TD.
The Broncos also featured a strong ground attack with Doug Martin rushing 19 times for 138 yards.
The Beavers (1-2) settled for 159 yards passing from Ryan Katz, who finished 12-of-26 with a touchdown.