The Sand Gnats, needing two wins in the series to claim a South Atlantic League Southern Division first-half championship, moved closer to the title with their fifth consecutive win.
The GreenJackets dropped their third in a row, slipping to the brink of elimination after spending the past month at the top of the division standings.
Augusta catcher Tommy Joseph struggled at times behind the plate allowing three passed balls that contributed to the unearned runs. Chris Dominguez and Ryan Cavan combined for back-to-back errors in the fifth to give Savannah a lead it didn't relinquish.
Savannah starter Armando Rodriguez got the win.