Morse smacked a two-run double and finished 1-for-2 with a walk and three RBIs as the designated hitter. He finished with a .375 average over the four games at Bowie.
Meanwhile, Rick Ankiel played center field and went 0-for-2 with a run scored and a walk, batting .333 over the series.
Morse can return as early as Tuesday from his lat injury. Ankiel (quad) is eligible to come off the disabled list April 14.
Outfielder Eury Perez went 2-for-4 with a triple, a run scored and two RBIs. Perez is batting .421 to start the season. Second baseman Jeff Kobernus went 1-for-3 and is hitting .412.
Danny Rosenbaum (1-0) was very impressive, notching the victory, tossing six innings, scattering four hits, allowing one run and one solo homer, no walks and one strikeouts.
Pat Lehman struck out two hitters and got three outs for his second save.
The Senators went 3-1 vs. Bowie in the four-game set.
Update: Low Single-A Hagerstown general manager Bill Farley tweeted that Ankiel and Morse will start for the Suns on Monday at home against Lexington.