The Generals (7-3, 4-1 ODAC) scored goals in the 15th and 18th minutes to take a lead they would not relinquish over the Hornets (2-9-1, 0-5).
The W&L defense was outstanding, holding SU to just four shots on the evening with two of those on-frame.
Washington & Lee pelted Shenandoah keeper James Dutcher with 24 shots, including 15 in the first half, with Dutcher making six saves.
The Generals also took 10 of the game's 12 corners.
Conor Starr, who had a game-high five points on two goals and one assist, had what proved to the game-winner in the 15th minute.
SU continues ODAC play on Saturday with a 7:30 contest against Hampden-Sydney.