W&L (6-1, 1-0 ODAC) scored its first goal 95 seconds in and took a 2-0 lead into halftime versus Shenandoah (0-7, 0-1).
The Generals scored goals in the 49th, 58th and 75th minutes to provide the final margin of victory.
W&L outshot SU 22-4 and had a 14-1 advantage in corner kicks.
Sweeney had eight saves in 65 minutes of action.
The Hornets step out of conference on Tuesday with a 7 p.m. home game against Frostburg State.