Campbell (6-7) overcame an early 9-0 deficit and used a 16-5 run ignited by a Reco McCarter 3-pointer to move out to a 51-37 lead midway through the second half.
Georgia Southern (7-8) fired back with a surge of its own to pull within one on a Brian Holmes 3-pointer with 2:03 remaining, but McCarter and Ray each hit layups to push the lead back to five.
After three Jelani Hewitt free throws, Ray and Kyre' Hammer each hit a pair from the stripe to ice the game.
The Fighting Camels shot 43.6 percent from the field and outrebounded Georgia Southern 37-27. Leonard had eight boards and Ryan hauled in seven.
Tre Bussey paced the Eagles with 18 points and Hewitt added 13.