Hagerstown took the early lead but fell behind 7-1 before Jason Columbus hit a three-run homer in the sixth to bring the Suns within three runs.
Travis Ishikawa doubled and Pat Dobson walked to lead off the ninth and chase reliever Javier Ochoa. Carlos Muniz came on and got Dayton Buller to fly out before walking Jay Knowlton to load the bases.
Tim Hutting, who led the Suns with three hits, got his chance with the bases loaded, but grounded into a double play to end the game.
Hagerstown took a 1-0 lead in the first off starter Brian Walker as Knowlton led off with a walk and took third on Hutting's double before scoring on Eddy Martinez-Esteve's grounder to short.
Capital City roughed up Ryan Callahan in his first start with two runs in the first as the Bombers loaded the bases after two outs before Shawn Bowman scored on a passed ball and Jabe Bergeron walked for a 2-1 lead.
Capital City took a 4-1 lead in the third on an RBI double by Blake Whealy and a run-scoring single by Hill.
The Bombers got back-to-back home runs - a two-run shot by Bergeron and solo shot by Jesus Lineres - off reliever Daniel Portorreal to make it 7-0.
Callahan lasted three innings, allowing four runs on five hits, before Portorreal allowed three runs in four innings.
Capital City starter Brian Walker (4-4) got the win despite allowing three runs in five innings.