For the second straight contest, SU (25-6, 11-4 ODAC) rallied from a six-run deficit.
The Eagles (24-10, 10-7) touched up Hornets starter Colin Morse for six runs on five hits, a walk and hit batsman in the second, but Shenandoah had an answer.
The Hornets scored five runs in the third, highlighted by a Jake Loew three-run HR, before taking the lead with four more in the fourth.
Abel Arocho, who had a two-run double immediately prior to Loew's dinger, had a two-run single in the fourth to put SU on top to stay.
The Hornets had two unearned runs in the sixth, with Loew driving in another run, to stretch its lead out to 11-8.
Bridgewater had an unearned run in the eighth but could get no closer.
Jones gave up two hits and issued two walks while Mossman gave up the unearned run and two hits. He also struck out one.
Arocho was 3 for 4 with four RBI while Loew made the most of his five at-bats by driving in five runs on the three-run HR, a groundout and a fielder's choice.
Shenandoah continues this road trip tomorrow with a 3 p.m. game at No. 19 Frostburg State.