Sarah Hopkins scored that lone goal in the 49th minute for GC (7-3, 4-0 USA South) to capture the win over the Hornets (6-5, 2-1).
Awarded a direct kick approximately 25 yards from SU keeper Kat Terza, Hopkins stepped up and drove the ball across the face of the goal and into the right side of the net for the game-winner.
Shenandoah had two significant chances following Hopkins' goal, but Pride keeper Shireen Unvala was able to come up with the save each time.
SU outshot Greensboro 7-3 for the game and also was awarded six of thr game's eight corner kicks.
The Hornets are on the road for the next three games, starting with the Southern Virginia game on Wednesday at 4:00.