Speas tallied the decisive score when he collected a weak clearance attempt at the top of the box and fired a shot through a crowd that found its way past United goalkeeper Bill Hamid.
Josh Williams scored in the first half for the Crew (2-1-1), who snapped United's 19-game home unbeaten streak.
Rafael scored D.C. (1-2-1).
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys