The Rams were almost knocked down to the elimination bracket in the second round but rally to beat Claflin 6-5.
Panthers led 3-1 after three innings but the Rams scored twice in the fourth and once in the fifth to take the lead 4-3.
Claflin went back in front in the sixth with two runs.
Roger Jones drove in Corey Reeves in the bottom of the sixth to tie the game.
Demarcus Price then singled in Reeves in the eighth with the go-ahead run.
Albany State plays at 1:00 p.m. Friday against the winner of the Stillman-Benedict game that was played late Thursday.
Other first round scores were Claflin 9-3 over Miles. Stillman beat Morehouse 16-12 and Benedict downed Tuskegee 15-5.