The win was the ninth in a row for Utah State (19-6, 9-2 Western Athletic).
Boise State (11-13, 2-9) dropped into last place in the nine-team conference.
Wesley scored nine of the Aggies' first 10 second-half points and his fast-break layup gave Utah State its first double-digit lead at 45-35 with 16:41 remaining. Quayle followed with two free throws and Nate Bendall added a basket to complete a 10-0 run that gave Utah State a 14-point lead with just under 15 minutes left.
Boise State used an 18-6 run to pull within 63-59 with 2:09 remaining on Anthony Thomas' layup. The Broncos got within two points twice in the final 20 seconds.
Thomas scored 15 points to lead Boise State.