Moore surrendered only one interception for the Broncos (1-0), who lodged their first win ever over a Southeast Conference school.
Boise State was helped by rushing touchdowns from D.J. Harper and Doug Martin while Kyle Efaw collected six passes for 53 yards and a score.
Georgia (0-1) got 235 yards on 16-of-29 passing from Aaron Murray, who passed for two scores and had one picked off.
Brandon Boykin turned in an 80-yard touchdown run and Orson Charles caught six passes for 108 yards and a score.