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.
Taylor scores 24, Incarnate Word rallies to 80-78 win in OT
Morgan Taylor scored 24 points, including a 3-point basket that forced a tie in regulation and a drive in the paint with 26 seconds left in overtime as Incarnate Word battled past North Dakota State 79-78 Saturday at the Islands of the Bahamas showcase.
Duquesne rallies to beat Radford 69-64 behind Williams
Eric Williams Jr. scored 11 of his 14 points in the second half and grabbed 10 rebounds for his 13th career double-double, Mike Lewis II added 15 points and Duquesne rallied to beat Big South Conference preseason favorite Radford 69-64 on Saturday.
Gibbs, Harvey key Irish over error-prone Tribe 73-64
T.J. Gibbs scored 18 points and D.J. Harvey added 15 to lead four Notre Dame players in double figures as the Irish beat error-prone William & Mary 73-64 on Saturday.