The score had been tied since the sixth inning when Werth worked a one-out walk in the 10th against Michael Dunn (2-2). A double by Laynce Nix sent Werth to third and he scored from there on LaRoche's fly ball to left.
Drew Storen (2-1) pitched the ninth inning to get the win and started the 10th as well. Storen gave up singles to Greg Dobbs and John Buck to open the inning but he remained in the game and got Omar Infante on a ground out to the mound.
After Storen struck out Wes Helms, Sean Burnett replaced Storen and got Chris Coghlan on a fly ball to center. It was Burnett's fourth save.
Washington was coming off a three-game sweep by Philadelphia. Jerry Hairston had three hits and an RBI for the Nationals.
Florida has lost three of its last four.