The Hornets (7-5, 2-2 ODAC) scored a pair of goals in the first 10 minutes to take a lead they would not relinquish over the Vixens (0-8, 0-4).
Freshman Alexandra Darrow, who led all scorers with three goals and four assists for 10 points, had both of the tallies in the opening stretch of the contest.
Senior Sarah DeLuca, off of a Darrow assist, closed the book on the first half scoring with a goal at 22:15.
Darrow had assists on both of Johnson's goals as well as Brock's.
SU outshot SBC 49-4 and had all but one of the game's 16 penalty corners.
Hornets keeper Sarah Clare made four saves and Vixens goalie Brooke Scott had 23 stops.
Shenandoah travels to Washington and Lee on Tuesday for a 5:00 ODAC contest.