McInerney took a 35-yard pass from substitute Sebastien Le Toux in the 75th minute, danced around defender Jalil Anibaba and slipped the ball by diving goalkeeper Sean Johnson.
The victory was the first in three matches for Philadelphia (4-3-3) and only the second in its last seven games. It was the fourth loss for the Fire (2-6-1) in the last six matches and the second straight game without a goal. Chicago has been shut out in five of its nine matches this MLS season.
This was MacMath's second shutout of the season, with Chicago's best chances coming from midfield. He kicked away Dan Paladini's point-blank boot in the 33rd minute and made a diving stop on Quincy Amarikwa in the 95th minute to seal the victory.
