The Nationals, who trailed 6-3 after seven innings, cut the deficit to 6-5 in the eighth on Ryan Zimmerman's two-run homer.
After the Marlins were held scoreless in the top of the ninth, a violent rainstorm crossed over Washington, forcing a delay of 2 1/2 hours.
Then with Heath Bell pitching after the game resumed, the first batter -- Werth -- sent a 3-2 pitch over the center field fence to tie it up.
In the 10th, pinch-hitter Corey Brown scored Ian Desmond from third on one-out single against Chad Gaudin (3-2), and the National League East-leading Nationals evened their three-game series.
Drew Storen (2-1) earned the victory with a scoreless top of the 10th.
Gorkys Hernandez and Giancarlo Stanton each socked solo homers for the Marlins.
Celebrity Breakups and divorces of 2014 [PHOTOS]