New York ended a four-game skid and dropped the Nationals a game below the .500 mark.
The Mets piled up 15 hits and put together four multi-run innings to make things easy for Dillon Gee.
Gee (4-6) gave up nine hits in seven innings, but limited the Nationals to a lone run. New York, meanwhile, roughed up starter Dan Haren (4-7) for five runs on seven hits in just four frames.
Byrd put New York in front with a two-run homer in the second and added a solo blast in the third to give him eight for the season. David Wright also had a two-run shot in the third inning and Anthony Recker drove in three runs overall -- two with a fifth-inning single and another with a seventh-inning double.