Nick Duncan added 17 on five 3-point shots for the Broncos (16-6, 6-3 Mountain West Conference).
The win snapped an 18-game losing streak in the Smith Spectrum for Boise State and extends its conference win streak to six games.
The Aggies knotted the score for the first time in the second half at 47 with 9:14 to play on free throws by Collette.
Marks nailed two free throws after a mad rebound scramble with 42 seconds to play to give Boise a 66-63 lead.
USU had a chance to tie in the final 20 seconds, but Darius Perkins missed both attempts. Webb then made two free throws to secure the win.