The WildCats (16-3, 7-3 ODAC) outscored SU 12-2 from the 10:38 to 4:33 marks to pull away from SU (3-16, 0-10).
Colton Hunt, the league's leading scorer, did most of the damage as he had nine of the 12 points in the spurt.
Shenandoah continued to battle, cutting the deficit to four points by the 3:09 mark as Eli McEathron scored five consecutive points, but Randolph answered with a 10-2 run to finish the first half.
Hunt again was the story, hitting a 3-pointer and a jumper in the final 12 seconds of the stanza.
The two teams played the second half relatively even, with RC outscoring its hosts 33-30, but the 'Cats held a double-digit lead for the remainder of the contest.
SU was able to get within 11 points on four occasions, the last with 13:56 remaining following a Sharif Almulla jumper at 13:56 left, before seeing the WildCats seal the victory with a 22-8 run over a span of 10:04.
The Hornets then finished the game by scoring 11 of the game's final 12 points, the last a Billy Brennan layup as time expired.
McEathron led the hosts with 13 points while Carithers added 11.
Hunt had a game-high 22 for the 'Cats.
Shenandoah travels to Eastern Mennonite on Wednesday for a 7:00 p.m.