Goals from Jack McInerney, Gabriel Gomez and Antoine Hoppenot overwhelmed Chicago, whose reply came from Dominic Oduro.
McInerney took on a pass from Danny Cruz to open the scoring with a low finish in the seventh minute, and then provided the headed pass that gave substitute Gomez space to double the lead in the 67th minute, lashing a shot across goal and into the top left corner.
Oduro cut the lead two minutes later, but the Fire had Guillermo Franco sent off soon afterwards, and they conceded for a third time with four minutes remaining when Antoine Hoppenot turned in a low cross from Michael Farfan with a smart backheel.
With three rounds of regular-season games to play, Chicago stand third in the Eastern Conference, only two points clear of fourth-placed DC United and four ahead of fifth-placed Houston Dynamo.
Three reach the MLS Cup play-offs automatically and the next two highest finishers play a match to decide which join the leading trio.
Chicago would have stood second, three points clear of the New York Red Bulls and in line for home advantage in their Conference semi-final, had they won.
The Vancouver Whitecaps were 4-0 winners over Chivas USA thanks to goals from Gershon Koffie, Dane Richards, Camilo and Barry Robson.
Vancouver cannot finish in the top three of the Western Conference