Shenandoah (13-15, 4-7 ODAC) needed a win over the Quakers (9-17, 3-8) in order to qualify for the eight-team tournament in its first season in the league.
Coach Jaime Terenzi's club did just that, winning 25-12, 21-25, 25-14, 20-25, 15-13 to advance while eliminating GC in the process.
SU used a 4-0 run early in the fifth to take control and eventually led 12-8 before the hosts were able to cut the deficit 13-12.
A Quakers kill kept the hosts in the match, but Haley Smith had her 15th and final kill off of another Brown set to give the match to the Hornets.
Parkes also had 17 digs.
The Pacers (13-16) won at 16, 23 and 21 in the match.
Haley Smith had seven kills, Rachel Gross five and Mary Harshman five for SU.
Shenandoah takes on Randolph-Macon on Wednesday at 7 in the opening round of the ODAC Tournament.