The Hornets (7-1, 1-0 ODAC) earned the win by winning 25-19 in the first, 25-16 in the third and 16-14 in the decisive fifth.
Randolph (2-9, 0-2) battled back with 25-17 and 25-8 wins in the second and fourth, respectively.
In the fifth, the WildCats had a 13-9 lead until SU rallied to tie at 13-13 behind a Megan Gillispie kill, two RC attack errors and a 'Cats ball handling error.
Randolph appeared to win it at 15-13 when Samantha Schambach had an attack that went wide, but a touch was ruled and the point awarded to the Hornets to tie at 14-14.
Freshman Blake Parkes paced the victors with 10 kills with Smith adding nine and Gillispie eight.
Jordan Templin had a match-high 13 kills for the 'Cats.
Shenandoah continues ODAC play with a 2:00 match Saturday versus Lynchburg.