Leading 24-21 at the break, the WildCats (7-8, 2-4 ODAC) scored 15 of the 23 points in the third quarter to pull away from Shenandoah (4-11, 1-5).
Randolph kept up the pressure in the fourth, outscoring the Hornets 23-10 over the final 10 minutes to provide the final margin of victory.
The 'Cats did all of their damage at the end of the third quarter – junior Kirstyn Arcata brought the Hornets to within one, 30-29, with a layup at the 2:31 mark only to see Randolph put forth an answer.
The hosts ended the stanza on a 9-0 run and then scored the initial four points of the fourth to push its lead out to 14, 43-29, with 7:55 to play.
Shenandoah would get no closer than 11 points the rest of the way.
Trailing by those 11 points, 49-36, following a Mia Moore jumper at 4:38, the Hornets saw Randolph score 18 of the game's final 21 points to post the 23-point victory.
The win snaps a three-game SU winning streak over the 'Cats in the long-time series.
Randolph had a 52-37 advantage on the boards with led to a 36-6 bulge in points in the paint.
SU shot 25 percent to 41 percent for the 'Cats.