Bryce Harper legged out a one-out double off Dana Eveland (0-1), then back-to- back walks to Wilson Ramos and Clint Robinson loaded the bases. David Aardsma entered from the bullpen and served up Desmond's deep fly ball to left.
Felipe Rivero (1-0) picked up the win for Washington, which has won seven straight against the Braves and five straight overall.
Nationals starter Jordan Zimmermann, who looked to snap a three-start losing streak, scattered six hits with three strikeouts over eight innings. He was in line for the win before closer Drew Storen blew the save in the ninth.
The Braves loaded the bases with consecutive singles from Nick Markakis and A.J. Pierzynski before an intentional walk to Joey Terdoslavich packed the bags. Kelly Johnson plated Markakis for a tie game with a sacrifice fly to center, but Terdoslavich was thrown out attempting to advance to second on the play. Andrelton Simmons grounded out softly to second to end the inning.
Shelby Miller was charged with a run on three hits with five strikeouts in seven innings of work for the Braves.
Atlanta had a pair of chances to score with runners in scoring position and two outs in the fourth and sixth innings, but Zimmermann got out of each jam unscathed.
Miller carried a perfect game into the fourth and faced the minimum through six innings, with Anthony Rendon breaking through with a one-out single in the fourth for Washington's first baserunner of the night.
The Nationals grabbed the lead in the seventh on Harper's bloop single into right. Denard Span led off with a walk and Rendon followed with a chopped single over Kelly Johnson at third. Yunel Escobar grounded into a force out that put runners at the corners before Miller jammed Harper, who muscled the pitch over the outstretched arms of Jace Peterson.