LaRoche also finished with three runs batted in for the Nationals, powering them to their second win in three games.
Ian Desmond launched a solo shot as Washington took the opener of a three-game interleague series.
Craig Stammen (2-0) was credited with the win despite yielding three hits and a run after taking over in the sixth inning for Gio Gonzalez, who had held the Chisox to one run over five frames.
Chicago made a run in the ninth inning on a two-run homer from Alex Rios -- who finished with three hits -- but could get no closer.
Jake Peavy (1-1) took the loss, yielding six runs on nine hits while striking out seven over 5 1/3 innings.
2014: The Year in Music [PHOTOS]