Philadelphia wasted no time in taking control of the match in the early stages, with McInerney opening the scoring in the seventh minute after good work from Danny Cruz.
Dan Paladini was unlucky to not equalise for Chicago before half-time when he struck the post with a free kick from 25 yards.
After the break it was Paladini who came closest to scoring for Chicago again, with Zac MacMath reacting well to block the midfielder's powerful effort.
However, the Union's lead was cut just two minutes later after a Dominic Oduro strike sparked hopes of a Chicago fightback.
Antoine Hoppenot added a third late on with a close-range finish and Chicago's night was made worse when Guillermo Franco was shown a red card for a bad tackle on Brian Carroll.