The Bobcats (1-0) scored all five goals of the first quarter and led 9-1 at the break over Shenandoah (0-1).
Frostburg led 8-0 when David Estoclet tallied for SU at the 5:26 mark of the second.
The Hornets saw FSU extend its advantage to 14-2 at the end of three before SU scored the final four goals of the contest.
David Estoclet rounded out the multiple point scorers with a goal and an assist.
Tyler Quinn had the 12 saves in his first start in goal for the Hornets.
The Bobcats outshot Shenandoah 38-21, had a 56-36 advantage in groundballs and won 16 of 23 faceoffs.
SU opens its home slate on Wednesday at 7 p.m. in non-league game against Hood College.