Mitchell Delfino, Joseph Rapp and Charles Jones had RBI singles in the 12th inning for Augusta, now 25-18.
Steven Okert (2-2) pitched scoreless innings in the 11th and 12th to pick up the victory.
Augusta starter Kendry Flores took a 3-1 lead into the ninth inning, but gave up a two-run homer to Eric Garcia that tied it up. Stephen Johnson came on to get the final two outs of the inning.
Augusta remains a half-game behind Lexington in the South Atlantic League’s southern division. Lexington beat Asheville 4-3 on Tuesday night.