It was the first win in Division I for the Spartans (1-7), who lost their first seven games all on the road.
S.C. Upstate led throughout, scoring the first eight points of the game and opening with an 18-6 run.
The Spartans led by 11 at the break and had their biggest lead of the game at 66-34 on Payne's fastbreak lay-up with 9:26 to go.
S.C. Upstate outrebounded Brevard 41-27 and turned 19 turnovers into 22 points.
Josh Chavis added 10 points for the Spartans.