Peter Vermes' men take sole possession of first place, though the Shield race will be tight after this weekend's matches.
The hosts took a lead in just the seventh minute. Under pressure for KC forward CJ Sapong, D.C.'s PErry Kitchen attempted a backpass, but it was intercepted by KC's Dom Dwyer, who then rounded goalkeeper Bill Hamid to finish into the empty net.
Despite conceding an early goal, United was no pushover as the Red and Black were desperate in their last chance for an away win in the 2013 season. Jared Jeffey had D.C.'s best chance of the night in the 15th minute but perhaps had too much time to waver and his breakaway shot was stopped at close range by Jimmy Nielsen.
The win gives Sporting (16-10-7) 55 points, more than any other team in the league, although New York, Portland and Salt Lake could equal or better that total with their games in hand.
D.C. (3-23-7) remains in last place in MLS.