Playing as the visitor Sunday afternoon, SU jumped on the Tigers for two runs in the top of the first to lead from start to finish.
Coach Kevin Anderson's club scored single runs in the third, fifth, sixth and eighth to take a 6-2 lead into the ninth.
Shenandoah needed nearly all of that as Hampden-Sydney scored two runs on three hits and two walks before senior reliever Michael Bugonowicz closed the door by striking out Devin Daugherty with a runner on first.
Bugonowicz came on with the bases loaded and nobody out and induced a 4-3 double play to put SU one out from victory. The Tigers followed with two hits, one with two strikes, to bring Daugherty to the plate with the tying run.
Junior southpaw Robert Klinchock (6-3) pitched the initial 5 1/3 to get the win. Klinchock allowed one run on six hits and three walks while striking out three.
Senior Jonathan Dance got the next eight outs before turning it over to Bugonowicz. The save was Bugonowicz' fifth of the season.
Tristan Baker matched Woolford's production with a 2-for-3 afternoon that included an RBI double in the fifth and an RBI single in the eighth.
Chase Smallwood also had two hits.
Shenandoah completes its home slate on Monday with a 6 p.m. non-league contest versus Penn State – Harrisburg.