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.
Purchase hits 5 3s, scores 23; Hawaii beats UC Riverside
Jack Purchase scored 23 points and hit five of Hawaii's 13 3-pointers and the Rainbow Warriors never trailed in their 87-64 win over UC Riverside on Saturday night.
Leonard lifts UC Irvine past UC Santa Barbara 83-70
Evan Leonard had a season-high 23 points as UC Irvine stretched its win streak to eight games, beating UC Santa Barbara 83-70 on Saturday night.
Fitts leads Saint Mary's (Cal) past Pepperdine 72-65
Malik Fitts had 25 points as Saint Mary's won its eighth consecutive home game, topping Pepperdine 72-65 on Saturday night. Jordan Ford added 20 points for the Gaels.