Byrnes hit an RBI double in the third and a two-run fifth-inning homer. Snyder had a one-run double in the third and a two-run double in the sixth.
The winner was reliever Esmerling Vasquez (1-1).
Chad Qualls recorded his eighth save.
Washington's Adam Dunn and Josh Willingham both homered twice, with Dunn driving in three and Willingham two. A run scored on a seventh-inning fielding error by Felipe Lopez, and Ryan Zimmerman had three hits to increased his hitting streak to 28 straight games for the Nationals, who had won three in a row.
The losing pitcher was reliever Logan Kensing (0-2).