Josh Currier scored with 1:04 remaining in the first overtime to give VWC (6-3, 3-0 ODAC) the comeback victory over Shenandoah (4-6, 0-3).
The Hornets led 9-6 after scoring all four goals of the third, but could only watch as the Marlins scored the initial three goals of the final stanza to tie the contest at 9-9 with 6:45 remaining.
Senior Aaron Paul then gave SU the lead again with an unassisted goal at the 4:30 mark; VWC ended up tying it on a John Roth goal 44 seconds before the end of regulation.
The Marlins won the ensuing faceoff and had four shots in the final 30 seconds of regulation, including two that hit the post, before Shenandoah was able to run out of the clock.
Both teams had shots on goal in the extra session, with Stephen LaTona denied by Rory Finnegan and Paul missing high before Virginia Wesleyan was able to get the Currier goal following a timeout and a missed shot.
VWC outshot the Hornets 70-31, scooped up 45 of the game's 77 groundballs and won 14 of 22 faceoffs.
Shenandoah goalie Ben Judy had 23 saves.
Paul led the Hornets with five goals and one assist for six points with LaTona adding two goals and two assists and Tilghman Sanders a goal and three assists.
SU is off until hosting Washington and Lee next Saturday at 2 p.m.