Philip Simpson of Byrnes scored a game-high 25 points including five three-point goals. Teammate Devonte Wright added 20 points.
Greer was led by Cam Woodruff with 16 points and Sam Gravley scored 13 points. Magic Moody did not play for the Yellow Jackets.
Greer led Byrnes by six points, 52-46 after three quarters but the Rebels outscored the Yellow Jackets 19-9 to secure the win.
Greer is 9-13 overall and Byrnes is 12-9.
Greer plays its final two games next week, both Class AAAA Region II games hosting Union County Tuesday and playing at rival Blue Ridge on Thursday.