Greg Van Sickler (8-1) pitched 6.0 innings, allowing one run on nine hits and one walk while going 3 for 4 at the plate with two home runs.
Van Sickler gave SU (26-2, 10-1 USA South) gave himself the early lead with a solo HR in the bottom of the first.
Averett (21-16, 5-6 USA South) actually outhit SU 15-12, but fell victim to three Hornets double plays.
Shenandoah scored two runs in the first, two in the third and one in the fourth before blowing things open with a five-run sixth.
Sophomore Kurt Krout provided the big blow in that sixth with a three-run double off the leftfield wall.
Van Sickler had led off the frame with his second solo HR - both shots (his fifth and sixth of the season) went to left.
In addition to Van Sickler's 3 for 4 day, Beall was also 3 for 4 and Clint DeHaven 2 for 5.
Eight of the nine Cougars at least one hit and seven of the nine had two hits each.
These two teams are back in action tomorrow at 1:00. Sophomore Vince Claudio (2-0) is the Hornets scheduled starter. An SU win clinches the program's first-ever USA South Conference regular season championship and a first-round bye at the upcoming USA South Conference Tournament.