Calicutt (2-1) surrendered just three hits on the day, striking out five and walking none. The win was Augusta's fifth in a row.
The GreenJackets (16-15) took a 1-0 lead in the second inning when Thomas Neal scored on Andrew Davis' two-out single off Braves starter Chad Rodgers. They added another run in the fifth on Ramon Corona's sacrifice fly, which drove in Jackson Williams.
Rome cut Augusta's lead in half in the eighth on David Berres' sacrifice fly off Andrew De La Garza.
The Braves put runners on first and second with two outs in the ninth, but Daniel Otero struck out Jon Gilmore looking for his fifth save of the season.