Trailing 1-0 since the first inning, the Cubs began a rally in the eighth when Dioner Navarro led off with a single against Drew Storen.
Then in the ninth against Rafael Soriano (0-1), Alfonso Soriano and pinch-hitter Julio Borbon each singled with none out. The pair were sent on a double-steal and Soriano scored when Nationals catcher Kurt Suzuki fired the ball past third base for an error.
Nationals starter Gio Gonzalez tossed seven shutout innings, allowing just two hits while walking one and striking out six.
Ryan Zimmerman provided Washington's only RBI.