Mitchell Parker threw six shutout innings for his first victory since June 16 for Washington, which has won back-to-back games since a five-game skid that matched a season high.
Gary Sánchez homered for the NL Central-leading Brewers, who dropped the final two of a three-game series and have lost four of five overall.
Milwaukee went 2-4 against Washington this year, the first time the Brewers lost a season series to the Nationals since 2015.
“They play us tough,” Brewers manager Pat Murphy said.
“They did the same thing to us in Milwaukee. They played really good and they played free.
We’re young and vulnerable and going through it a little bit. You can make all the excuses you want with injuries and inexperience, but every team goes through it and we’re going through it.”
García put Washington up in the first when he ripped Tobias Myers’ 3-1 fastball to center for his 13th home run of the season.
The second baseman, who homered in Saturday’s 6-4 victory, had his seventh multi-hit game in his last 10 outings and is hitting .398 (33 for 83) with six homers and 17 RBIs since July 3.
