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, but he was furious with his team after the game.
"We started the game like [expletive] and we somehow managed to finish it off even worse," Magee said, according to MLSSoccer.com. "I think we thought the game was tied or we were winning and we were just going to sit back and we were content. Unfortunately, we were down 2-1, so it wasn't a very good gameplan."
Magee blamed the Fire's loss on their unwillingness to send players forward.
"I can't remember a time in the second half where, during the run of play, we had three players in our attacking box," Magee said, according to MLSSoccer.com. "It's a joke. It's unacceptable. Basically, it seemed like we were just content to leave the game 2-1.
"We weren't going to send numbers, we weren't going to take gambles, we were just going kind of say, 'It's 2-1, it's hot. Cool, let's go home and enjoy the rest of our Sunday.' It makes me sick."
Information from The Associated Press was used in this report.