With the win, the Dallas club remains undefeated and leads the Western Conference with 10 points.
In the 68th minute, Dallas' Chris Gbandi was ejected from the game after fouling Wizards' Davy Arnaud.
Kansas City then grabbed the equalizer in the 92nd minute as Alex Zotinca fired a shot from 6 yards out that hit off the crossbar and bounced into the home team's net.
Two minutes later, substitute Pitchkolan scored outside the penalty to seal the win for Dallas and record his first goal of the season.
Swim Week Miami Beach 2014 [PHOTOS]