The Tigers scored the next 13 goals of the game to take a lead they would not relinquish over SU (6-7, 2-4).
Eric Sawyer broke up that H-SC run with an unassisted goal 11 seconds prior to halftime.
The Tigers ended the third quarter on a 3-0 run and scored the first goal of the fourth.
The two teams split the final six goals of the game with Sawyer, Brooks and Troy Hubbard scoring for SU.
Hampden-Sydney outshot Shenandoah 47-25, won 20-of-31 faceoffs and scooped up 40 of the game's 68 groundballs.
SU hosts Randolph-Macon on Wednesday at 7 p.m.