Moreno converted a penalty kick for his fifth goal of the season and Gomez added his second goal. Josh Wicks denied Chicago striker Brian McBride in the second half on a penalty kick and United held on for their second straight win.
Chicago (5-3-6) opened the season with an 11-game unbeaten streak, but lost its third straight to fall out of first place. D.C. (5-2-7) has lost just once in its last 10 games.
Chicago's Marco Pappa scored his fourth goal of the year in the 33rd minute.