The game was scoreless heading into the fourth before the visitors turned six hits into a four-run lead.
Shelbyville answered in the bottom half of the frame when a Ben Jones was followed by Burchett's second two-bagger.
Post 23 broke the game open their next trip to the plate, scoring six runs to move ahead 7-4, highlighted by Drew Turner's double.
Stephon Ransom and Chase Johnson both singled and scored for some insurance for Shelbyville in the sixth.
Jones and Burchett also tallied a single and a run apiece in the eighth.
Bryant Prater gave up nine hits and four walks while striking out four over six innings of work to earn the 'W' for Post 23. Hunter Bates hurled the final three frames.
Jones totaled three hits. Turner paired his double with a seventh-inning single.
Shelbyville is scheduled to host Pulaski Post 60 for a doubleheader on Saturday at 2 p.m.

