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.
No. 10 Kentucky working out kinks, hosts North Dakota
Tenth-ranked Kentucky returns to action Wednesday against North Dakota with coach John Calipari trying to move his basketball team forward by taking a huge step backward.
It's about a five-hour ride from Clinton, Miss., to Auburn, Ala., but the gap between the Mississippi College and Auburn on the hardwood is more like 5 million miles.
No. 1 Duke hears the noise, hosts Eastern Michigan
The noise could become louder for Duke.