Strasburg (11-4) allowed just four hits and left the game with a 5-1 lead.
He then had to watch as Washington relief pitching loaded the bases with walks in the eighth before getting out of the jam. The Nationals blew a 9-0 lead in Strasburg's start Friday.
After the shaky eighth inning, in which a New York run scored on a Jordany Valdespin ground out, Tyler Clippard pitched a 1-2-3 ninth for his 18th save.
The only run Strasburg allowed came on a second-inning Ike Davis home run.
The Nationals added an unearned run in the fourth when Espinosa scored on a play in which Mets catcher Josh Thole was charged with an error. Washington's Adam LaRoche made the score 5-1 with a two-run home run in the eighth.