After winning the opening set at 18, Shenandoah (11-11, 3-6 ODAC) found itself down 2-1 as the hosts won sets two and three at 23 and 18, respectively.
The Hornets roared back in the fourth to win at 12, setting up a decisive fifth set.
The two teams then traded the lead five times and had 13 ties in the fifth before SU emerged victorious with a 19-17 triumph.
Shenandoah had the first opportunity to win the fifth, serving with a 14-13 lead, only to see HU (7-18, 1-8) stave off defeat with a pair of points to take a 15-14 lead.
Shenandoah fought off a match point of its own at 16-17 and use that point to start a 3-0 run that clinched the victory.
Sophomore Rachel Gross was at the service line for both of those points and Hollins was wide on two consecutive kill attempts to give the Hornets the victory.
The Hornets had 112 digs in the match with Nicole Mueller pacing a group of six women in double figures by posting 29. Harshman had 22 to back up Mueller.