Arnaud found the net just before halftime with his sixth goal of the season, curling a running shot past Fire goalie Andrew Dykstra on assists by Bunbury and Kei Kamara.
The Wizards (11-12-6) made it 2-0 in the 80th minute on Bunbury's tally.
Ninth-place Kansas City broke a three-game losing streak and kept its dwindling playoff hopes alive. The Wizards came into the game needing to win their last three contests, coupled with two losses by Colorado, to sneak into the post-season.
Chicago, which has been eliminated from playoff contention, fell to 8-13-8.