Gordon (4-2) earned the win with a scoreless eighth. Brad Lidge pitched the ninth for his 11th save in 11 chances. Lidge walked two, but got Felipe Lopez to ground out with runners on first and third to end the game.
The hit also ended the 12-inning scoreless streak of Washington reliever Jon Rauch (2-1).
Dobbs' hit kept Philadelphia from being shut out in consecutive games for the first time since Sept. 11-12, 1999, and kept the Phillies from their first four-game losing streak since Aug. 22-25, 2007.
The late-inning offense came after Philadelphia's Cole Hamels and Washington's Jason Bergmann each pitched seven scoreless innings.
Hamels gave up four hits, walked two and struck out 11 - tying a season high. It was the eighth time in nine starts Hamels had lasted at least seven innings.
Bergmann allowed five hits and struck out five before being removed for a pinch-hitter.
It was Bergmann's second-straight seven-inning outing since returning to the Nationals after a stint in the minors.
Bergmann had been sent to Triple-A Columbus after posting a 10.45 ERA and 0-1 record in two April starts. Since being recalled on May 14, Bergmann earned his first win of the season in a 1-0 game at New York on May 15 and had another strong outing Tuesday.
Philadelphia's best chance to score a run against Bergmann came in the seventh inning.
Pedro Feliz and Carlos Ruiz singled. Hamels' sacrifice advanced Ruiz to second and Feliz to third - the first time a Philadelphia baserunner had reached third base.
After Washington intentionally walked Jimmy Rollins to load the bases with two out, Bergmann got Shane Victorino to line out to center field, ending the threat.
The Nationals had runners on first and second with two out in the seventh and eighth innings, but each time the runners were stranded.
In the seventh, Aaron Boone pinch-hit for Bergmann and became Hamels' 11th strikeout victim to end the inning. In the eighth, Gordon got Lastings Milledge to ground out.
