The Black-and-Red landed a 1-0 result at the RFK Stadium courtesy of an injury-time winner from Chris Pontius as Ben Olsen's side got the better of Bruce Arena's outfit who were without star strikers Robbie Keane and Gyasi Zardes.
The victory saw DC move up to second place on the Eastern Conference table as the Galaxy dropped to seventh in the West.
Lions ace Kaka assisted Pedro Ribeiro for the first of the visitor's goals in the 29th minute before levelling less than a minute later with a customary cool finish after Ignacio Piatti and Jack McInerney had given the Impact the ascendency.
Kelyn Rowe scored a brace as last season's runners-up New England Revolution defeated San Jose Earthquakes 2-1 at the Gillette Stadium for their first win of the campaign as Sporting Kansas City edged newcomers New York City 1-0 at Yankee Stadium.
Reigning Golden Boot winner Bradley Wright-Phillips was on target as New York Red Bulls beat ten-man Columbus Crew 2-1 while Robert Earnshaw netted a late winner on debut for Vancouver Whitecaps as they beat Portland Timbers 2-1.
Chicago Fire got the better of Philadelphia Union 1-0 thanks to Adailton's first-half winner, Real Salt Lake scored a dramatic late victory over Toronto FC to land a 2-1 result, Houston Dynamo and Colorado Rapids played out a 0-0 draw as did league leaders FC Dallas and Seattle Sounders.
2015 MLS season scores - Week 4
New York City: 0 Sporting Kansas City: 1 (Ike Opara 12') Yankee Stadium, New York City, New York - 27,454
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