The Falcons held a 31-30 lead at intermission. Boise State pulled ahead on Marks' 3-pointer - the first shot of the second half - and never trailed again, although the final 20 minutes saw five ties and no more than a single-digit lead.
Marks shot 4 of 5 from 3-point range and had six assists. Duncan finished 6 of 8, all from beyond the arc for the Broncos, and James Webb III added 10 points and five steals.
Boise State (14-6, 4-3 Mountain West) shot almost 58 percent from the floor, and 14 of 22 on 3-pointers.