Shenandoah (9-15, 5-10 ODAC) led for 37:49 of regulation, but saw VWC (16-8, 9-6) outscore SU 9-2 down the stretch to force the five-minute overtime.
Lamont Steward made the first two buckets of OT for the Marlins to give the hosts a lead they would not relinquish.
SU had a chance to win it in regulation, but sophomore Dalon McHugh's runner from just outside the 3-point line went off the back rim and the Hornets could not get off another shot before the buzzer sounded.
The Hornets were in total control early, scoring 26 of the initial 31 points of the game to lead 26-5 with 7:36 to play in the first.
Virginia Wesleyan scored 14 of the final 21 points of the first to cut the deficit to 14, 33-19, by halftime.
The two teams played virtually even for the first eight minutes of the second and Shenandoah held a 10-point, 51-41, with 11:54 to play following a Malcolm Clark layup.
Clark, who had a career-high 38 points, scored 22 of those points in the second half to give his squad a chance to win.
Unfortunately, VWC, which shot just 25 percent (6 of 24) in the first half and missed nine of its 10 3-point attempts, shot 61 percent from the field and 54 percent from behind the arc to key the comeback.
McHugh had 13 points to back up Clark.
Steward had 23 points off the bench to pace the hosts.
Shenandoah completes its regular season on Saturday with a 4 p.m. Senior Day contest versus Roanoke.