Stutz made 7 of 9 field goals and 8 of 8 free throws.
Eastern Kentucky (11-6, 3-1 Ohio Valley) trailed 33-32 at halftime, but opened the second half with a 13-2 run to make it 45-35 with 14 minutes to play.
Corey Walden made back-to-back layups and Stutz made consecutive 3-pointers during a 14-2 spurt that gave the Colonels a 20-point cushion with 8 minutes left.
SIU-Edwardsville (7-10, 3-3) trailed by double digits the rest of the way.
Walden scored 19, on 8-of-14 shooting, and Timmy Knipp added 14 for Eastern Kentucky, which shot 66.6 percent (14 of 21) after halftime.
Kris Davis led the Cougars, who shot 33.3 percent in the second half and finished with 23 turnovers, with 15 points.