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.
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Wisconsin business offering 'therapeutic cuddling' forced to close