Denzel Richardson scored 13 points for Eastern Kentucky (17-10, 9-5 Ohio Valley), while Ja'Mill Powell and Timmy Knipp added 12 points apiece.
After a first half where the teams weren't separated by any more than five points, Knipp's dunk with 12 seconds before the half gave Eastern Kentucky a 33-30 lead.
EKU scored the first eight points after intermission to open a 41-30 advantage. Austin Peay used an eight-point run later to draw to within five with 6:45 left, but the Colonels responded with the next six points - including Richardson's 3-pointer - to push the lead back to nine.
Paul Jackson made 5 of 6 from the line down the stretch to seal the win.
Ed Dyson and Josh Robinson led Austin Peay (7-21, 2-12) with 13 points apiece.