Steve Lombardozzi had a three-run triple and Michael Morse had two hits and two RBI for the Nationals, who extended their lead to five games over second-place Atlanta in the NL East.
Edwin Jackson (6-6) shut out the Brewers on eight hits over seven innings with one walk and four strikeouts, and also scored twice for Washington.
Milwaukee Yovani Gallardo (8-8) gave up seven runs on seven hits with two walks and six strikeouts over five innings.
The Brewers -- who have lost seven straight and eight of their last 10 -- got word Thursday from General Manager Doug Melvin that pitching ace Zack Greinke will definitely be traded before Tuesday's non-waiver trade deadline.
The Nationals took control early, scoring four runs in the second inning, starting with LaRoche's 19th home run of the season.