The WildCats (3-5, 1-1 ODAC) won their first-ever ODAC contest on a Jon O'Hara unassisted goal with 3:43 remaining.
Randolph needed O'Hara's tally as SU (5-3, 0-2) roared back from a 9-3 halftime deficit to tie the contest at 9-9 with 8:37 remaining.
Shenandoah had held the 'Cats scoreless from the 6:02 mark of the second (also on an O'Hara goal) until the hosts got the game-winner in the waning moments.
Freshman Matt Justice figured in four of the six SU goals that tied the game.
Fowler scored again 16 seconds later, this time off of a Scotty Sweigart assist, before Justice had a natural hat trick with goals at 13:47, 9:21 and 8:37.
The game was virtually even, with RC outshooting SU 41-39 and the Hornets winning 12 of 22 faceoffs. The two teams each had 14 saves and committed 18 turnovers.
Shenandoah did have a 44-34 advantage in groundballs.
The Hornets host Hampden-Sydney on Saturday at 1:30 in another ODAC contest.