Casey beat goalkeeper Jimmy Nielsen with a left-footed shot from just outside the area for Colorado, which has four ties and a loss since June 5.
Casey has seven of Colorado's 17 goals.
Davy Arnaud scored in the 20th minute for Kansas City, which last won in Colorado on June 9, 2004.
Kansas City has two ties in seven visits since then and is 1-8-6 overall at the Rapids.
Craig Rocastle found Arnaud alone along the sideline and the Wizards captain made a move on Colorado goalkeeper Matt Pickens just outside the crease before sending a low shot past Pickens' left hand.
Kei Kamara couldn't finish a chance to make it a two-goal lead early in the second half. His shot from inside the area went just right of the right post in the 54th minute.
Casey also hit the left post and missed a wide open net in the 89th minute.