The Generals (4-8, 2-3 ODAC) got a Taylor Zusi tally 2:34 into sudden-victory overtime to steal the victory from Shenandoah (7-6, 2-3).
SU had scored the opening goal of the game on a Sarah DeLuca tally in the 17th minute and took this one-goal lead into the halftime break.
W&L knotted matters at 1-1 on a Lindsey Purpura tally in the 57th minutes before Shenandoah reasserted its advantage four minutes later when Liz Grover scored unassisted.
Unfortunately for the Hornets, this lead would last only 3:44.
Lauren Boone, who had set up the hosts first goal of the contest, scored with 4:01 remaining to help force the extra session.
SU had the initial shot of the OT, by Amber VanHorn following a penalty corner, but Generals keeper Kristen Kyne made her seventh (and final) save to keep W&L in it.
Ninety-four seconds later, Zusi finished off a Claire Townsley feed to give Washington & Lee the victory.
Shenandoah outshot its hosts 19-9 and had 12 of the game's 20 corners.
The Hornets continue this roadtrip on Thursday with a non-league game at St. Mary's of Maryland.