Shenandoah (12-1, 1-1 ODAC) was a 9-8 winner in the opener before LC (10-7, 2-2) was a 13-4 victor in the nightcap.
Senior Neil Dutton, who had three hits, two RBI and two runs scored, led off the Shenandoah ninth with a single to right center before being lifted for Silvestre.
Silvestre moved to second, and then third, on a pair of wild pitches, setting Goode up to provide the game-winning RBI with his single.
Shenandoah needed the final inning heroics as LC scored three unearned runs in the top of the ninth to tie the game at 8-8.
Goode's RBI also capped a game in which SU rallied from a 5-0 deficit with three runs in the fifth, three more in the sixth and two in the seventh.
Dutton and Goode both finished the game 3-for-5 with two RBI while Donnie Forgacs also drove in a pair.
Senior Tyler Hott (1-0), the fourth pitcher of the game for Shenandoah, earned the win with 1/3 of an inning of relief work. He struck out one and gave up one hit.
In game two, Lynchburg erased a 2-0 deficit with a four-run fifth off of SU starter Zach Teeple. LC extended its lead by getting into the Shenandoah bullpen for nine runs (eight earned) on eight hits and four walks in 4 1/3 innings.
Teeple (3-1) was charged with the loss after allowing four runs on six hits and three walks in 4 2/3 innings of work.
Shenandoah is up next on Wednesday in a 4 p.m. non-league home contest versus No. 3 Cortland (N.Y.) State.