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.
Jim Calhoun, who has a career record of 873-380 and led UConn to three national titles before retiring in 2012, has been hired as coach at Saint Joseph.
Pac-12 commissioner Larry Scott believes a tentative ruling making show-cause orders illegal in California would threaten NCAA membership for state schools.
Guard James Bouknight, ranked 87th in the ESPN 100, is the first player from the Class of 2019 to commit to UConn and first-year coach Dan Hurley.