Penn led 45-35 at the half and 51-41 with 17:17 remaining. The Quakers then went on a 15-2 run to take their biggest lead, 66-43, with 13:54 to go.
The Citadel went on a 14-2 run and closed within 68-57 on a three-point play by Demetrius Nelson with nine minutes left.
However, Kach hit a 3-pointer and Eggleston a layup, pushing the lead to 73-57. The Bulldogs never got closer than 14 points the rest of the way.