The Aggies (30-3) led most of the game but had to hang on as Boise State mounted a late charge.
Wesley, who also hauled down nine rebounds, responded by scoring nine of his points in the final 5 minutes to preserve the victory, which gave Utah State its second WAC Tournament title in three years and an automatic bid to the NCAA Tournament.
Nate Bendall added 16 points and six boards for the Aggies, who shot 53.1 percent from the field.
La'Shard Anderson led the Broncos (20-12) with 18 points.
Ukrainian protestors topple Lenin statue [VIDEO]
Selena Gomez drops F-bomb, walks off stage during Jingle Ball performance