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.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.