With two out in the inning, Mica Lewis singled and stole second. Jackson then hit a 2-0 pitch by Chuck Ricci (4-1) over the wall in left.
Reading (14-14) had taken a 3-1 lead after three innings with Gene Schall, who finished 4-for-6, knocking in two runs with RBI singles, and Sam Taylor driving in a run on a groundout.
Bowie (17-12) tied it 3-3 with an unearned run in the seventh, and it stayed that way until Jackson's third homer of the season.
Chuck Marchok (1-0), the fourth Reading pitcher, got the win.