GreenJackets starter Kyle Vazquez (4-2) shutout the Braves through six innings but surrendered a single, double and Whitmer's triple in the seventh to blow a 1-0 lead.
Rome added a run in the eighth when Cory Harrilchak walked, stole second and third and scored when GreenJackets third baseman Chris Dominguez failed to cover third base and catcher Tommy Joseph's throw bounced into left field.
Rome starter Brett DeVall (2-2) got the win after allowing two hits and no earned runs in six innings pitched. David Hale struck out seven in three hitless innings of relief to get the save.
Augusta's lone run came in the fourth inning when Rome committed three errors. The GreenJackets left a runner at third base in the inning, one of six runners stranded by the home team.