In a game that had five lead changes and nine ties, Shenandoah (3-4, 1-1 ODAC) sandwiched a 7-0 run around the end of the third quarter to take a lead it would not relinquish versus Randolph (3-4, 0-2).
After Sarah Wright tied it for the WildCats with her layup at the 50 second mark of the third, Shannon Kuhn put SU on top to stay with a layup of her own 46 seconds later.
Jordan Sondrol, who led all scorers with 20 points, opened the fourth with a 3-pointer followed by a Kirstyn Arcata layup that gave the Hornets a seven-point, 46-39, lead with exactly nine minutes remaining.
The lead would eventually reach nine following a Kuhn jumper at 6:25 before Randolph made matters interesting with a 12-6 run that put the 'Cats down just one, 58-57, with 25.9 seconds left.
Randolph fouled on the next two inbounds and McKenzie Mathis effectively clinched the win by hitting all four free throws.
The 'Cats, following an SU foul with 2.3 seconds remaining, made 1-of-2 from the line and got the rebound. Fortunately for the Shingleton Gymnasium faithful, their 12-footer from the baseline was long as the buzzer sounded.
"The free throw difference was huge for us, and we have been steady from the line all season, but we definitely had ice in our veins down the stretch."
The Hornets were 20-of-26 from the line to 10-of-18 for Randolph.
Mathis and Ashley Stone each had 11 to back up Sondrol.
Shenandoah steps out of conference on Saturday for a 2 p.m. contest at Mary Baldwin.