Nick Duncan scored a career-high 17 points and made five 3-pointers and Ryan Watkins added 15 points and 16 rebounds for the Broncos (13-5, 3-2 Mountain West).
Marks blocked a breakaway layup attempt by Marcel Davis with 37 seconds left and came back down the court to hit the basket that gave Boise State a 75-74 lead.
Jarred Shaw matched a season-high with 24 points for the Aggies (12-5, 2-3) but missed with under five seconds left. Preston Medlin added 16 points.
The Aggies led 71-66 after Shaw's basket with 2:56 to play but Marks made four baskets down the stretch. Anthony Drmic added two free throws and Marks made one in the final 3.6 seconds.