The victory was only Kansas City's second in the past seven matches, giving SKC 30 points.
Kansas City's two goals were scored 2 minutes, 14 seconds apart.
Feilhaber scored his first of the season in the sixth minute, hammering a right-footed shot from 16 yards when a throw-in by defender Matt Besler deflected off two players and ended up at his feet.
Chicago goalkeeper Paulo Tornaghi couldn't stop that shot, and seemed surprised by midfielder Zusi's nonchalant 20-yard shot soon after. It curled over Tornaghi and into the upper right-hand corner.
Mike Magee cut the margin to 2-1 in the 38th minute.