Shenandoah (18-9, 9-7 ODAC) was a 2-1 winner in the opener before completing the sweep over the Panthers (19-13, 10-6) with an 8-6 win in the nightcap.
Junior Gerard DePhillips had the save in both contests.
Klinchock (4-3) scattered one run on six hits in 7 2/3 innings before DePhillips got the final four outs to record his ninth save of the spring.
Klinchock struck out nine and did not walk a batter.
DePhillips worked around a one-out single in the ninth by striking out the final two hitters.
Thompson and Robert Marcelle both had two hits.
Carlton Redd (2-2) took the loss after allowing two runs (one earned) on six hits in 7.0 innings. He struck out two.
The Hornets scored two runs in the first, fifth, seventh and ninth to outlast FC and complete the sweep with the 8-6 win.
Keegan Woolford put SU on top to stay with a two-run home run. The dinger is his third of the week and fifth of the season.
The home run made a winner of Michael Robst (2-1), who threw 1.0 innings of scoreless relief.
In the ninth, DePhillips posted his 10th save by striking out the first hitter and getting a flyout to right. Following a hit-by-pitch and an infield single, he closed it out with a groundball to short.
DePhillips is now one save from tying Tyler Hott '17 for the SU and ODAC season saves record.
Will Davis (2-2) took the loss in relief. He allowed two runs on three hits in 2.0 innings.
Shenandoah hosts Marymount on Tuesday at 4 in non-league action.