Moore threw three scoring strikes in all, going 13-of-18 through the air for 196 yards for the Broncos (4-0, 1-0 WAC).
Doug Martin hauled down Moore's other TD pass and rushed 94 yards and a score on 10 carries, helping BSU extend its winning streak to 18 consecutive games.
Boise State also got rushing touchdowns from Jeremy Avery, Jarvis Hodge and Mike Coughlin while piling up a 608-208 advantage in total yards of offense.
The Aggies (0-4, 0-1) was led by Matt Christian, who went 5-of-14 passing for 63 yards with an interception.
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