Tracy then lined a hit past diving second baseman Darwin Barney, scoring two runs.
LaRoche finished 4-for-5 with a homer for Washington, which improved to 2-0 to start the season.
Ryan Mattheus (1-0) earned the win with a scoreless seventh inning and Henry Rodriguez picked up his first save for the Nats.
Matt Garza tossed six innings for Chicago, allowing two runs on five hits.
Reed Johnson stroked a two-run triple in the Cubs' loss.