The Fire's win was their third in their past four matches and moved them to .500 (10-10-4) for the season with 34 points in the Eastern Conference.
Sporting K.C. fell to 11-9-6 and remains tied with New York on top of the East with 39 points.
Hunter was about a foot off the ground when he scored. The goal, in the 13th minute, finished off a furious offensive start for the Fire.
Kansas City, with striker Claudio Bieler on the bench after a five-match scoreless streak, failed to rally.
In earning his fourth shutout of the season, Johnson turned back midfielder Graham Zusi's bouncing shot from near the penalty kick spot in the 54th minute and defender Seth Sinovic's 5-yard kick in the 84th minute.
Chicago nearly had a second goal in the 72nd minute, but Nielsen got a fingertip on substitute Patrick Nyarko's hard shot and deflected it off the crossbar.
The Fire played with Mike Matkovich as acting head coach. Head coach Frank Klopas was serving a suspension for his ejection from last Saturday's loss at New England.