Thompson (1-0) struck out 10 in tossing the first 8.0 innings of game one while Scimanico (2-0) had six strikeouts in 7.0 innings of work in game two.
Thompson allowed three hits and one walk in earning his first victory of the spring with the lone run that Scimanico allowed in game two was unearned.
Scimanico scattered five hits in his second victory of the week.
SU had a combined 26 hits in the two games, including 16 in the nightcap.
Sophomore John Wilt had five hits in 11 at-bats over the doubleheader and also drove in one run in both games.
Senior Daniel Freshley plated the Hornets first run of the day with a solo HR in the bottom of the second in game one before driving in another run with a groundout one inning later.
Paul drove in three runs and Pardo two.
Phillip Morse, who pitched the final 1 2/3 of game two, had three strikeouts.
Shenandoah is back in action tomorrow at 2 p.m. with a non-league doubleheader against Penn St. - Altoona.