Rodriguez (9-7) did not walk a batter and fanned six in his best start this season. He also helped himself with an RBI single in the fifth inning.
Closer Jose Valverde equaled a franchise record by earning his 44th save.
Atlanta averted shutout when Brent Lillebridge scored on Corky Miller's fifth-inning groundout.
Kelly Johnson had two of the six hits for the Braves, who finished the season with a 72-90 record.
Losing pitcher Mike Hampton (3-4) gave up three earned runs and four hits in six innings with no walks and five strikeouts.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys