The Braves have won a franchise-best eight straight games in Washington and 10 of 12 overall. They entered Sunday tied with Philadelphia for the NL East lead.
Jesse Chavez (3-2) allowed two runs on three hits, and Will Smith worked a scoreless ninth to earn his 25th save. Smith allowed two walks but struck out Victor Robles and Juan Soto.
The Nationals have lost a season-high seven straight and are 10-30 since July 1.
Washington tied it with a three-run third. Robles had an RBI single, Adrian Sanchez scored on a wild pitch from Braves starter Drew Smyly and Soto had an RBI sacrifice fly to score Robles.