The sixth-seeded Stags (25-7) got 12 points from Ryan Olander and moved on to a second-round match-up against Kent State.
Andy Ogide led third-seeded Colorado with 13 points. Greg Smith scored nine points and grabbed 15 rebounds.
Colorado State shot 32.2 percent from the field but was within one point with 8 seconds to play. Fairfield's Derek Needham hit one of two free throws on the next possession, and the Rams' Wes Eikmeier missed on a final shot from 3-point range.
Celebrity Families of 2014 [PHOTOS]