Ross Detwiler (4-5) hurled six shutout innings, surrendering only four hits while walking two and fanning four.
Henry Rodriguez, Tyler Clippard and Drew Storen (42nd save) completed the whitewash.
Atlanta's Mike Minor (5-3) was saddled with the loss despite allowing only one run on six hits over 4 2/3 frames.
The setback was the 10th in 15 games for the Braves, who saw their lead in the NL wild card race dwindle to just one game over the St. Louis Cardinals.
The Cards bested the Chicago Cubs 3-2 Sunday.