Demarcus Croaker added 14 points on 7-of-10 shooting with five rebounds and four assists.
Moss hit a layup and a 3 and Croaker followed with back-to-back dunks to give the Racers the lead for good. The 9-0 run in a two-minute span broke a 23-all tie, and Murray State (8-8, 2-1 Ohio Valley) led 32-25 at the half.
After the break, Moss hit another 3 to make the score 44-33 with 15:21 to play. Christian Cunningham's jumper cut the deficit to 52-44 with 9:15 left but the Gamecocks couldn't get closer.
Murray State shot 7 for 14 from the free-throw line and Jacksonville State was just 3 of 5.
Malcolm Drumwright had 14 points, seven rebounds and six assists for Jacksonville State (5-14, 1-3).