Scherzer (15-6) bounced back from his worst start of the season, also against the Braves last week, when he walked six and was roughed up for seven runs in an 8-2 loss.
This time, Scherzer struck out seven and walked only one while throwing 83 of 112 pitches for strikes.
Ryan Madson pitched around trouble in the eighth and Sean Doolittle finished with a perfect for his 22nd save, his 19th in as many chances since the Nationals acquired him from Oakland on July 16.
Ryan Zimmerman had three hits and drove in a pair of runs for the NL East champion Nationals.
Rookie left-hander Luiz Gohara (1-2) surrendered four runs and 11 hits in 6 1/3 innings.