Moreno capped a 40-yard run with a shot from about 20 yards out that he put by goalkeeper Tony Meola and inside the right goal post.
It was Moreno's first goal since a season-opening victory over San Jose, a span of six games.
D.C. United superstar Freddy Adu did not start. The 14-year-old sensation was a second-half substitute and failed to register a shot.
Nick Rimando had three saves for D.C. United (2-2-3).
Kansas City (2-2-2) fell to 0-2-0 on the road.