The bullpen pitched three scoreless innings, with Jonathan Papelbon earning his ninth save with a scoreless ninth.
The Phillies took a 5-3 lead with two runs in the eighth off reliever Drew Storen.
Michael Young, not the fleetest of foot, scored from first on Delmon Young's two-out RBI single. Delmon Young drilled a hit past a diving Adam LaRoche at first. Michael Young easily beat Bryce Harper's two-bounce throw to the plate.
"Obviously I'm the go-ahead run out there, so the second he hit behind me I knew I was going to do everything I could to score," Michael Young said.
Delmon Young picked up teammate Ryan Howard, who had made the second out by striking out for the fourth time.
"It was a fastball that ran up and in," Delmon Young said. "I was looking away and the ball ran up and in, and it happened to stay inside and be right on the line."
Delmon Young stayed on first. He said he was held by first base coach Juan Samuel. But it didn't matter when pinch-runner Michael Martinez scored on Brown's RBI double.
Chad Durbin earned the win. With the score 3-3 and runners on first and second and two outs in the seventh, Durbin came in and got Ian Desmond to fly to center for the third out.
Durbin allowed a bunt single by Kurt Suzuki and a walk to Tyler Moore to begin the eighth. After getting Steve Lombardozzi on a liner to short, he was replaced by Jeremy Horst, who got Chad Tracey and Denard Span to fly out.
The Phillies received a workmanlike outing from rookie Jonathan Pettibone, who allowed three runs on nine hits in six innings. He became the first Phillie to allow three earned runs or fewer in each of his first seven career starts since Charlie Hudson in 1983.
After Nationals righthander Dan Haren struck out four batters in a row, Brown hit a first-pitch home run to right in the second inning.
"He left the ball up and I had to take advantage of it," Brown said.
"He is swinging good. I say just leave him alone and let him hit," manager Charlie Manuel said.
The next batter, Erik Kratz, duplicated the feat, also off the first pitch. It was the fourth time this season the Phillies have hit back-to-back home runs.
The Nationals got a run back in the third on LaRoche's two-out RBI single to center. Pettibone averted further damage when he got Suzuki on a weak grounder to first with the bases loaded.
Washington tied the score in the fourth on Span's RBI single to right after he just missed hitting a home run.
Jimmy Rollins gave the Phillies a 3-2 lead with an RBI double to right in the fifth, knocking in Pettibone, who had crushed a two-out double to center. It was the first extra-base hit of his career.
LaRoche tied the score in the bottom of the inning with a solo home run to left, his eighth of the year.
Contact Marc Narducci at firstname.lastname@example.org. Follow on Twitter @sjnard.