The win is the first for Shenandoah over Lynchburg since December 6, 1995 and snaps an eight-game losing streak to LC.
Baltimore's bucket, his fifth of the contest, was the only field goal of overtime. Jalyn Jarrett hit one of two from the line at 1:26 to put SU up by four before Lynchburg scored its final two points on a pair of Zach Burnett free throws with 1:05 remaining.
In the final 15 seconds, Lynchburg sandwiched a turnover and a missed layup around a Baltimore free throw to provide the final margin of victory.
Shenandoah forced overtime by making up a seven-point deficit in the final 2:47 of regulation. Senior Malcolm Clark, who led all scorers with 19 points, got the rally started by hitting four straight from the line make it 66-63 with 2:34 left.
SU began to foul on the ensuing possession, and the strategy worked to near perfection as LC missed four of its final eight free throw attempts in regulation. Down four, 67-63, Jarrett hit a 3-pointer from in front of the Lynchburg bench with 14 seconds remaining to make it a one possession contest.
After another 1 for 2 showing at the line by the hosts, Derrick Perry was fouled as he corralled a rebound of Jarrett 3-point attempt from nearly the same spot as his successful shot seconds earlier. With 1.6 seconds showing on the clock, Perry calmly swished both free throws to knot the game at 69-69.
Lynchburg's ¾ court heave as the buzzer sounded hit the back wall and the two teams headed to OT.
In addition to Clark's 19, Baltimore chipped in with 16 points.
Clark had his third double-double of the year thanks to 11 rebounds.
Lynchburg had a 52-44 advantage on the glass and shot 36 percent to 35 percent for Shenandoah.