The Generals (4-3, 1-0 ODAC) broke open a two-goal game with an 11-1 run in the middle of the contest.
After Michael Brooks brought the Hornets (2-3, 0-1) to within two, 4-2, with a goal off of a Devon Weaver assist with 4:25 to play in the first period, W&L held SU to just one goal in the next 43:42 of game time.
Weaver and Brooks figured in that lone tally with Brooks setting up Weaver at the 3:15 mark of the second to make the score 9-3 in favor of the Generals.
Washington & Lee answered with the final two goals of the second and posted all four goals of the third to lead 15-3 after three.
Brooks led the visitors with two goals and one assist for three points with Schott posting two goals and Weaver a goal and an assist.
W&L outshot Shenandoah 53-24, won 18-of-27 face-offs and had a 44-26 advantage in groundballs. Weaver and Sam Gerhart led SU in that final category with three each.