The Blazers jumped out to four-run lead and then fought off the Gamecocks in the end to earn an 8-5 win and improve to 27-21.
Jamal Austin had three hits and Jonathan Merritt drove in three runs to lead UAB.
Mark McKinley (1-0) struck out five of the seven batters he faced to earn his first win of the season, and JSU's Jordan Beistline (7-2) took the loss.
Kyle Bluestein finished with three hits, while Davis and Eberle each added a pair of hits for the Gamecocks.
The Gamecocks (28-17) visit at Ohio Valley Conference foe Tennessee Tech this weekend.