Belmont led 29-27 at the half but made eight-straight points after the break to pull away. The Stags (4-6) came back within two points, 56-54, after Steve Johnston made one of two free throws with 6:36 left to play.
Egekeze sparked a 10-2 run that put the Bruins back up by double figures. Belmont shot 17 of 28 (60.7 percent) in the second half.
Marcus Gilbert led Fairfield with 18 points, and Tyler Nelson added 14. Kevin Degnan chipped in 12 points. The Stags struggled at the free-throw line, shooting 53.8 percent (7 of 12) and 35.3 percent from the floor.