Edwin Jackson, who had not won any of his previous eight starts, ended that skid by holding down the Mets over seven innings.
LaRoche hit his ninth homer of the year in the first inning and added a sacrifice fly in the seventh.
Jackson (2-3) gave up all three New York runs, two of them earned on three hits. His last win had come on April 14 against Cincinnati in his second start of the season.
Tyler Clippard worked around a ninth-inning walk for his fifth save.
Washington has captured the opening two games of the series after dropping four out of five. The Mets have lost three straight.
Jeremy Hefner (1-3) took the loss, giving up four runs on seven hits in six innings.