Mayes was 9-of-15 shooting while Williams made 6 of 11 from the field and hit all 12 of his free-throw attempts. Marcus Barham added 20 points for FAMU (8-23, 7-8 Mid-Eastern Athletic Conference).
South Carolina State (10-20, 6-9) made four more (27) field goals than the Rattlers, but was outscored 26-18 from the free-throw line, where FAMU shot 81.3 percent.
The Rattlers are tied with Morgan State for seventh in the conference standings -- one game behind North Carolina Central. South Carolina State fell into an eighth-place tie with Howard.
Niagara wins season-opener, beats St. Bonaventure 80-72
Marvin Prochet had 20 points and 10 rebounds to help Niagara win its season opener with an 80-72 victory over St. Bonaventure on Monday night.
Youngstown State beats D-III Heidelberg 106-83
Garrett Covington scored 21 points, Olamide Pedersen had 14 points and 10 rebounds and Youngstown State beat Division III-member Heidelberg 106-83 on Monday night.
Carter scores 24, Ohio beats Campbell 81-73
Jason Carter scored 24 points, Doug Taylor had 14 points and 10 rebounds, and Ohio beat Campbell 81-73 on Monday night.