DC and RSL took to the field at RFK Stadium on Saturday but the match was stopped in the 28th minute due to storms with the game scoreless.
When the clash resumed the next day, RSL came out on top thanks to Luis Silva's 64th-minute strike.
After a goalless first half, which saw DC's Kofi Opare rattle the crossbar with a header, Silva pounced on Marcelo Sarvas' misplaced clearance to unleash a half-volley past Bill Hamid.
With the win, eighth-placed RSL moved within three points of the playoff spots in the Western Conference.
DC, meanwhile, remain 10 points adrift at the bottom of the Eastern Conference.