Morse (4-0) earned his second victory over Washington & Lee (22-10, 10-5 ODAC) this season with the Hornets (20-6, 8-4) first complete game of the season.
Morse scattered seven hits and two walks while striking out two in turning in the victory.
Offensively, SU scored one run in the first and three more in the second to stake Morse to a four-run lead.
Coleman led off the game with a walk and advanced into scoring position on an Abel Arocho single to right.
SU scored three runs on just one hit and a W&L error in the third. Nate Loman and Ryan Glendon drove in runs in the frame with Loman lacing a single through the left side and Glendon drawing a bases loaded walk.
Loman scored the final run as Tyler Hott reached on an error with the bases loaded.
The offense was more than enough for Morse as he retired the side in order in the third, fourth, eighth and ninth innings while seeing his defense turn inning-ending double plays in the second and seventh.
Morse retired the final seven batters in order.
Shenandoah steps out-of-conference Wednesday for a 4 p.m. home contest versus Messiah.