Moore completed 28-of-34 passes for 261 yards and three touchdowns against one interception for the Broncos (1-0), who had never previously defeated a school from the SEC.
"It was a very exciting game," said Moore. "You see Georgia play in big games when you grow up and to have an opportunity to play them in a game like this is just a lot of fun. We were fortunate to come out on top."
Boise State, which finished 12-1 as the toast of the WAC a season ago, was buoyed by rushing touchdowns from D.J. Harper and Doug Martin.
Kyle Efaw reeled in six passes for 53 yards and a touchdown and Matt Miller had five receptions for 57 yards and a score for the new Mountain West Conference denizens, who next play September 16, at Toledo.
Georgia, coming off a disappointing 6-7 campaign, received a respectable effort from Aaron Murray, who completed 16-of-29 passes for 236 yards and two scores against an interception.
Brandon Boykin had an 80-yard touchdown run and Orson Charles caught six passes for 109 yards and a score for the Bulldogs (0-1), who host South Carolina next Saturday.
"Obviously we knew going in they were pretty darn good," said Georgia coach Mark Richt. "They just beat us tonight. They were better than we were."
The Bulldogs struck first, as Boykin ripped off an 80-yard touchdown run with 8:39 remaining in the first quarter.
Boise State punted on its first three possessions, but finally broke through with 3:02 left in the opening quarter, when Moore connected with Miller for a 17-yard touchdown pass, capping a six-play, 58-yard drive.
Moore was intercepted by Branden Smith at the Georgia nine-yard line late in the second quarter, but Murray gave to ball back three plays later with a pick to Jerrell Gavins. Moore capitalized, leading the Broncos on a seven-play, 51- yard drive which culminated with a 12-yard scoring strike to Efaw, giving Boise State a 14-7 lead at the half.
The Broncos carried the momentum out of the tunnel, taking the ball 76 yards down the field on their opening possession. Martin's seven-yard touchdown run capped the drive.
Blair Walsh missed a 54-yard field goal attempt on the Bulldogs' next possession and Moore's three-yard touchdown pass to Tyler Shoemaker put Boise State on top 28-7 with 3:10 remaining in the third quarter.
Facing a 4th-and-2 late in the third, Murray found a streaking Charles for a 36-yard touchdown strike to give the Bulldogs and their raucous Georgia Dome crowd life.
Moore again responded with poise, leading Boise State on a 76-yard drive that lasted 4:36, and which Harper closed with a one-yard touchdown plunge.
The sophomore Murray proved seasoned himself, responding with a 51-yard touchdown pass to Malcolm Mitchell on Georgia's next series. The Bulldogs got no closer, however, as their remaining two drives ended in fourth-down incompletions at the hands of an active Boise State defense.
Boise State spent the previous 10 campaigns in the Western Athletic Conference where it captured an unprecedented eight league titles and sported a 75-5 record...The Broncos were winless in four previous games against SEC opponents...The game marked just the second meeting between the two teams. The first game came in 2005, when the Bulldogs downed Boise State 48-13.