Gabriel Gomez and Antoine Hoppenot also scored to help Philadelphia (9-15-6) win for the second time in three games after an eight-game winless streak. With head coach Frank Klopas serving a one-game suspension, the Fire were coached by assistants Mike Matkovich and Leo Percovich.
Dominic Oduro scored for Chicago (16-10-5), which lost its second straight and remained tied with New York for second place in the Eastern Conference, five points behind Kansas City with three matches remaining.
Philadelphia opened the scoring in the 7th minute as McInerney took a pass from Danny Cruz, split defenders Jalil Anibaba and Arne Friedrich, and hammered the ball behind goalkeeper Sean Johnson.
McInerney set up Gomez for the second goal in the 67th minute as Gomez's kick flew into the upper far corner of the net as Chicago defender Austin Berry partially screened Johnson.
Chicago pulled to 2-1 two minutes later when Dominic Oduro's slow shot caught Philadelphia goalkeeper Zac MacMath away from the right post, and rolled into the net.
Hoppenot beat Johnson with a deflection at the 87-minute mark.