The Cougars (8-3, 1-1 USA South) erased a 2-0 deficit with one run in the fifth and two in the sixth to down Shenandoah (5-3, 1-1).
The Hornets cut a four-run deficit in half with two runs in the ninth, but left runners on second and third as the game ended.
Both teams had seven hits on the day.
Shenandoah committed three errors that AU was able to convert into two unearned runs off of SU starting pitcher Cory Nelson (0-2).
Nelson allowed five runs (three earned) on six hits and one walk in 7 1/3 innings. He struck out two before turning it over to classmate Patrick Moore.
The run that Moore allowed was also unearned.
Nelson was 1 for 4 with a run scored as he also served as the team's designated hitter.
Cody Moore was 3 for 3 and Matt Mitchell 2 for 3 for the victors.