Joe Peluso scored what proved to be the game-winner in the 51st minute before Logan Paussa tallied in the 56th and 61st minutes to provide the final margin.
Paussa's first goal came via penalty kick.
The Pride outshot Shenandoah 23-12 and had 10 of the game's 12 corners.
SU falls to 2-9-1 overall and 0-3 in the USA South with the loss.
Shenandoah continues USA South Conference play with a 7:00 game Wednesday night at No. 2 in the nation Christopher Newport.