It was the third complete game this season for the Phillies, who stayed 1½ games back of the NL East-leading New York Mets.
The Nationals tied the Kansas City Royals for the longest losing streak in the majors this season. The skid is the franchise's longest since the Montreal Expos dropped 12 straight from Aug. 13-27, 1976.
Ronnie Belliard collected two more hits for Washington, which has the worst record in the major leagues at 44-83. Belliard is batting .444 (24-for-54) this month.
The Nationals have been shut out 19 times this season.
Greg Dobbs hit a two-run homer off Collin Balester (2-6) in Philadelphia's three-run fifth. Jayson Werth, who hit the winning home run on Tuesday, added an RBI double.
Myers, who threw 119 pitches, got some help from his defense when left fielder Pat Burrell threw out Ryan Zimmerman at the plate in the first for his 12th outfield assist.
The Phillies took a 1-0 lead in the third without registering a hit. With runners on first and second and one out, second baseman Emilio Bonifacio fielded Jimmy Rollins' sharp grounder and threw to newly acquired shortstop Anderson Hernandez at second. Hernandez then made an errant throw to first trying to complete the double play, allowing Chris Coste to score.
The Nationals got Hernandez on Wednesday to complete the trade that sent reliever Luis Ayala to the New York Mets.
Balester gave up four runs, three earned, and seven hits in six innings.
Notes: Cole Hamels has Philadelphia's other two complete games this season. ... Orlando Magic guard Jameer Nelson, a former star at nearby Saint Josephs University, threw out the first pitch. The game drew a sellout crowd of 45,166, the 16th in a row and the 42nd this season at Citizens Bank Park.