On the game-winning play, McInerney placed a shot past outstretched Fire goalkeeper Sean Johnson following through ball over Chicago's back line from Sebastien Le Toux.
The tally was an MLS-best seventh goal of the season for McInerney as the Union improved to 4-3-3 with the victory.
The Fire (2-6-1) lost their second straight and were held scoreless for the sixth time this season.
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