The Nationals scored a run in the ninth to keep the game alive and eventually halted a three-game losing streak.
Washington wasted a scoring chance in the 10th, but came through in a big way one inning later. Ryan Zimmerman doubled with one out, Adam LaRoche was walked intentionally and Werth drew a walk as well to load the bases.
That brought up Desmond, who hit a 2-2 pitch over the wall in left-center off Michael Stutes (2-1).
Drew Storen (2-1) worked the 10th inning to get the win and Rafael Soriano survived a one-out single in the 11th in a non-save situation.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Ray Liotta sues skin care company over use of likeness