Greensboro (16-9, 7-5 USA South) earns a date with No. 6 Averett by virtue of its win over Shenandoah (4-21, 2-10).
SU and the Cougars actually tied for sixth place in the league, but Averett won the coin flip for the No. 6 seed.
Shenandoah will play at No. 2 N.C. Wesleyan on Tuesday at 7:30 in the quarterfinal round of the USA South Conference Tournament.
On Saturday, the Pride took a 37-21 lead into the halftime lockerroom thanks to a 10-2 run to finish the opening stanza.
GC, which owned a 26-14 advantage on the glass, used this bulge to outscore SU 9-0 in second chance points in the first 20 minutes.
Greensboro also forced the Hornets into 16 first half turnovers and scored 14 points off of those giveaways.
Shenandoah, as has been its custom all season long, continued to fight coming out of the intermission.
The Hornets were able to cut the deficit into single digits on two different occasions, but a pair of Pride runs clinched the contest for the hosts.
With their lead down to nine points following a Bryce Mitchell layup with 14:50 remaining, GC hit consecutive 3-pointers to reassert control of the game.
The Pride eventually pushed their advantage out to 20 points before SU scored the final seven points of the game to provide the final margin of victory.