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.
Indiana guard James Blackmon Jr., who averaged 15.8 points in 13 games before being injured last season, has withdrawn from the NBA draft.
Isaiah Briscoe has decided to withdraw from the NBA draft and will return to Kentucky for his sophomore season. Marcus Lee intends to transfer.
The Big 12/SEC Challenge will again feature Kansas and Kentucky, this time at Rupp Arena. That's not the only exciting matchup in next season's midseason conference showdown.