The Union fell behind to a Josh Wolff strike a minute before the interval but a Perry Kitchen own goal had the sides level just four minutes after the restart.
DC went ahead again after 58 minutes when Andy Najar fired home, but the Union fought back for a second time with Carlos Ruiz bagging the equaliser six minutes from time.
The Union's slip opened the door for the New York Red Bulls to go to the summit but they, too, could only manage a 2-2 draw in their encounter with Western Conference outfit the San Jose Earthquakes.
Joel Lindpere fired New York ahead after seven minutes but goals by Khari Stephenson (37) and Steven Lenhart (68) turned the match in San Jose's favour.
Lindpere popped up again to level the scores after 85 minutes, while San Jose's frustration was compounded in the last minute when Bobby Burling was dismissed for a second bookable offence.
The draw leaves New York two points behind the Union in the east having played one game more.
Third-placed Columbus Crew lost ground on the Eastern Conference leaders as they fell to a 2-0 loss at FC Dallas.
Brek Shea (58) and Goncalves Jackson (76) scored the goals for Dallas, who sit second in the west, a point behind leaders the Los Angeles Galaxy having played one game more.
Andy Iro picked up a second booking for Columbus after 82 minutes.
Sporting Kansas City climbed to fourth place in the east after a 2-1 win at Western Conference strugglers the Portland Timbers.
CJ Sapong (15) and Aurelien Collin (19) put Kansas City in charge, and although Darlington Nagbe pulled one back for Portland it could not spark a fightback.
In another intra-conference encounter, Chivas USA drew 1-1 with the Chicago Fire.
Dominic Oduro put the Fire ahead after 26 minutes but Nick LaBrocca ensured the hosts a share of the spoils with his 46th-minute leveller.