Ryan Schott, who finished with three goals and three assists for six points, set up Brooks for that initial tally.
Brooks scored again at 4:15 before Schott made it 3-0 at 2:54. Both of those goals were unassisted.
Randolph (0-10, 0-4) scored its first goal 71 seconds before the first quarter buzzer.
SU turned the game into a rout by scoring all three of the game's second quarter goals and five of the six scored in the third.
The WildCats scored their lone goals of the second half at 7:19 of the third and 11:09 of the fourth.
Shenandoah outshot the 'Cats 45-17, won 13-of-21 face-offs and had a 26-25 advantage in groundballs.
Jason Simpson had four saves in 56:27 of action.
The men are back in action on Wednesday in a 4 p.m. non-league game at Ferrum.