The Hornets (6-2, 3-0 USA South) scored all 12 goals in the first half and cruised to the win over NCWC (0-5, 0-4).
Wesleyan got its initial goal at 28:17 of the second before the Hornets ripped off the next four goals to take a 16-1 lead with 13:36 remaining.
Grover, off of an Amy Rollins pass, completed the day's scoring for the victors.
Shenandoah had 12 different women register at least one point with Kosmowski, Sisson and Grover all scoring hat tricks.
Samantha Donaghy had a game-high five points on one goal and four assists.
SU outshot its hosts 33-5, owned a 19-9 advantage in groundballs and won 18 of 21 draws.
The Hornets won all 13 draws in the first half.
Shenandoah is back in action on Wednesday night in a non-league game against Hood. Opening draw on Sprint Field at Shentel Stadium is scheduled for 7:00.