Shenandoah (6-10, 2-6 ODAC) had tied the game at 6-6 following an unassisted Drew Brooks goal with 8:09 remaining in the third.
GC answered with four straight, scoring at 5:10, 3:58 and 3:24 of the third and 14:46 of the fourth to pull away from the Hornets.
The run was the second of the game for the Quakers – with the game tied at 3-3, the hosts closed out the first half with a three-goal spurt.
SU responded with the initial three goals of the second half, capped by that Brooks goal that tied the game at 6-6.
Brooks set up classmate Stephen LaTona at 11:04 of the fourth to make the score 10-7, but this would be as close as the Hornets would get the rest of the way.
Shenandoah held a 41-34 advantage in shots, 33-24 in groundballs and won 11 of 21 faceoffs, but Guilford goalie Thomas Deane made 20 saves to keep his side on top.
Hornets goalie Ben Judy had 12 saves.
Shenandoah completes its season on Wednesday at Washington and Lee.