Shenandoah (2-0, 2-0 ODAC) was an 11-2 winner in the opener before taking the nightcap 8-1 over Roanoke (1-4, 0-2).
Mossman allowed four hits and one walk while striking out three.
Thompson pitched the initial 3 1/3 innings and allowed two unearned runs on on two hits and seven walks.
Thompson, the 2014 ODAC Pitcher of the Year, struck out two.
The Hornets scored at least one run in all but the first and six innings; coach Kevin Anderson's squad broke open a 4-2 ballgame with a three-run fifth.
McDaniel proved all of that fifth-inning offense with a 3-run HR.
All nine hitters in the SU lineup either hit safely or drove in a run.
Shenandoah scored four runs in the first and two more in the third before riding the pitching performance of junior Michael Scimanico (1-0) in the nightcap.
Scimanico allowed an unearned run on three hits and two walks in 6.0 innings of work in game two.
Overby had a solo HR to cap the four-run first.
Freshley drove in three runs.
Shenandoah is back in action on Wednesday at Washington and Lee.