The win also extends Dallas' unbeaten streak to 17 and forges an impressive 12-game stretch without defeat on the road.
The Hoops took a two-goal lead shortly after the 10-minute mark.
First, David Ferreira cheekily chipped the ball into the box, where Marvin Chavez blasted into the near corner first-time. Then Atiba Harris put his body in harm's way to prod the ball clear of Jimmy Conrad and set Milton Rodriguez free. Rodriguez took a touch to steady himself at the top of the box and then slotted home with his left peg.
Kansas City was perhaps showing the early fatigue from a thrilling 4-3 win over the Houston Dynamo on Wednesday.
"We scored early," FCD coach Shellas Hyndman said after the match. "We worked all week on finishing on a small field, and then we worked on a lot of defensive heading. We watched what Kansas City does, and they are so direct.
"We also recognized that the Wizards were tired, playing their third game is seven days. The field conditions didn’t help them because it just made their legs heavier and heavier. Our game plan went the way we thought it would. We worked all week on it."
Despite the heavy legs, the Wizards mustered some life, sending some warning shots at Dallas goalkeeper Dario Sala.
Kei Kamara tried first, flicking a ball up under tight marking in the box and volleying it straight at Sala's chest. Shavar Thomas came close as the second half opened, planting a header on Ryan Smith's free kick delivery that whizzed inches wide of the upright.
Smith got in on the action just before the hour mark and managed to halve the deficit. His low drive in the box bounced off two separate players before ricocheting into the net.
Cunningham's goal 10 minutes from time killed off the match. Ferreira again provided the service, his 12th assist of the season, good for second in the league. Kansas City complained that Cunningham was offside, but replays showed Thomas had kept him on, before the 34-year-old finished from a tight angle.
The win gives Dallas the third best record in the league, just four points off the Los Angeles Galaxy. The Wizards, however, have a five point hole to climb out of with five games remaining to make the playoffs.
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