Senior Michael Bugonowicz tossed a complete game seven-hitter to pitch the Hornets (15-6, 6-3) to its fifth win in as many outings.
After W&L (9-17, 2-10) scored one run in the second, SU tied it with a single run in the fifth before putting up a three-spot in the sixth.
Woolford and Nussman each had two hits on the day.
The offense was more than enough for Bugonowicz (3-1), who had 83 strikes in his 125 pitches thrown as he struck out four and walked just one. He retired the Generals in order in the fifth, sixth, seventh and ninth innings and faced just two batters over the minimum after the fourth.
Nate Cohen (0-1) took the loss for W&L. He allowed four runs (two earned) on four hits in 1.0 innings of work.
Shenandoah is back in action on Thursday in a 2:30 non-league contest at York (Pa.).