The win evened the three-game series and gives the Phillies another chance to reach .500 in Sunday's finale - when they can also catch the Nationals for second place in the NL East.
Young walked and came home on Delmon Young's single to the right-field corner, stretching his hand across the plate to beat Bryce Harper's throw to break a 3-all tie. Pinch-runner Michael Martinez then scored on Brown's double to right-center.
The runs came off Drew Storen (0-1), the latest failure for a Nationals bullpen that manager Davey Johnson said "keeps me up more than the offense" - a strong statement considering that Johnson has vowed to stop shaving until his lineup breaks out of its collective hitting slump.
Chad Durbin (1-0) got two outs for the win, but was removed with one out in the eighth after allowing a bunt single and a walk. Jeremy Horst pitched out of the jam and Jonathan Papelbon worked the ninth for his ninth save.
Starters Dan Haren and Jonathan Pettibone both went six innings. Haren had quite the eclectic line: six innings, three runs, 10 strikeouts, one walk and four hits - all for extra bases. Brown and Erik Kratz hit homers on back-to-back pitches in the second inning, and Pettibone and Jimmy Rollins pounded back-to-back doubles to produce a run in the fifth.
Pettibone, a rookie yet to lose a decision over seven starts, was also mowing them down, matching his career high with six strikeouts while scattering nine hits and three runs. He allowed single runs in the third, fourth and fifth.
Denard Span had three hits, including an RBI single, while Adam LaRoche had an RBI single and an opposite-field homer for the Nationals, but it was hardly the offensive outburst Johnson has been seeking during his razor boycott. The 70-year-old manager decided to keep letting his facial hair grow despite a modest five-run output in Friday night's win.
"My wife said I could keep it one more day," Johnson said before the game. "The players want me to keep it. They think it looks better."
Asked if he thinks it looks better, Johnson said: "With the fuzz I've got? It's gray. You kidding me? You can't hardly see it, if you've got my eyes. I can't see it unless I put my glasses on."