The LC Hornets (9-1-3, 4-1-2 ODAC) outshot SU (11-4, 5-1) 27-1 in claiming the victory.
Lynchburg got what proved to be the game-winning goal in the sixth minute on a Marina Clark to Samantha Bagherpour tally.
Shenandoah goalkeeper Erin Septer, who finished with 12 saves, kept her side in it by making six of those stops in the first half.
The hosts put the game away in the 88th minute as Caitlin Mertens knocked home a rebound of a Marisa Inglisa shot.
Septer dove left to stop Inglisa's attempt, and after the ball squirted away from her following the save, had no chance as Mertens tapped the ball into the open net right from the doorstep.
Lynchburg also had an 8-2 advantage in corner kicks.
"Lynchburg deserved to win today," SU coach Liz Pike said. "These games are about one-on-one battles and LC won 95 percent of those today. It was a disappointing loss, but we will learn from it and get better."