Josh Thole's RBI double in the top of the 10th had seemed to hand the Mets a 4-3 victory, but the Nationals -- who also had rallied in the bottom of the ninth on Danny Espinoza's RBI single to extend the game -- staged another comeback.
Jhonatan Solano singled off Tyler Byrdak (2-1) to start the inning and came home with the tying run one out later on Bryce Harper's triple. Zimmerman and Ian Desmond were intentionally walked to load the bases and Byrdak induced Adam LaRoche to ground out, with Harper being forced out at the plate.
Beato relieved, and with Tyler Moore batting, uncorked a wild pitch, allowing Zimmerman to come home with the game-winner.
Ryan Mattheus (3-1) earned the victory after recording the final out in the top of the 10th for National League East-leading Washington, which took the opener of a three-game series.
New York's Jordany Valdespin smacked a three-run pinch-hit homer in the ninth off Nationals closer Tyler Clippard to forge a 3-3 deadlock.