The Nationals made the most of their seven hits to back up a 10-strikeout effort by Gio Gonzalez.
LaRoche cleared the bases by hitting reliever Evan Meek's first pitch to right for a double.
Gonzalez (5-1) gave up three runs on four hits over seven innings. Henry Rodriguez struck out one in a perfect ninth for his ninth save.
Erik Bedard (2-5) took the loss, surrendering four runs on six hits in six innings with seven strikeouts.