Cunningham hit 6 of 7 shots from the field and Martin knocked down 5 of 7 as the Gamecocks (5-2) connected on 30 of 56 attempts.
Branden Johnson was the lone player in double figures for the Hornets (0-8) with 10 points. He added seven rebounds. Alabama State made just 22 of 62 shots (35.5 percent) from the field, but connected on 20 of 22 free throws (90.9 percent).
Jacksonville State trailed 14-12 midway through the first half, but Martin made back-to-back layups to spark a 13-0 run and the Gamecocks led 37-22 at the half. Maurice Dunlap's 3-pointer stretched the lead to 29 points with 12 minutes to play and the Gamecocks cruised from there.
Alabama State has lost 15 in a row, the longest active losing streak in Division I.
Jason Burnell had four of Jacksonville State's 11 blocked shots.
Before he won an Oscar, Mahershala Ali played college hoops at Saint Mary's College
Back then he was a feisty guard known as Hershal Gilmore; now he's one of Hollywood's top actors and a favorite to win his second Academy Award
Queta scores 23 to carry Utah St. over New Mexico 71-55
Neemias Queta had 23 points and 10 rebounds as Utah State topped New Mexico 71-55 on Wednesday night.
San Diego State stuns Caroline, No. 6 Nevada 65-57
Jeremy Hemsley and Devin Watson scored 15 points apiece for San Diego State, which shut down Jordan Caroline and stunned cold-shooting No. 6 Nevada 65-57 Wednesday night, beating the Wolf Pack for the third straight time.