Shenandoah (15-5, 6-2 USA South) broke a 4-4 tie with two runs in the bottom of the eighth and then held on as GC (15-9, 3-5) attempted to rally in the ninth.
Designated hitter Steven Pfeiffer got the GC ninth started by being hit on the first offering from SU reliever Matt Riegler.
Anthony Catherina then singled before Grant Kelly cut the deficit in half with a double to center to score pinch runner Tony Fulsom.
Riegler, who was the winning pitcher on Saturday, then bore down and struck out Aaron Navarro, Josh Powell and Dan Melton to end the contest.
Melton went down looking on a 2-2 pitch.
SU, which trailed 4-1 after the Pride scored four unearned off of Hornets starter Cory Nelson (2-3) in the fourth, rallied with one run in the fourth and two more in the fifth to tie it.
Shenandoah scored its two runs in the eighth on two hits, a walk and a crucial Greensboro error at second base.
Lucas had the victors first run with a solo HR in the third.
Brian Robbett took the loss for Greensboro, allowing two unearned runs on two hits and one walk in one inning of work.
Nelson gave up four runs (all unearned) on three hits and four walks in 8.0 innings.
It was Riegler's third save of the spring.