The 20-year-old punished the Chicago Fire for the second Saturday in a row, again finishing off service from Sebastien Le Toux.
This time, the Union went up early, in the third minute, and no prizes will have been awarded for guessing the scorer. McInerney connected with Le Toux's cross after the Frenchman's corner was cleared and played back to him by Bakary Soumare to score his league-leading eighth goal of the season.
Wells Thompson was sent off in the 63rd minute after receiving his second yellow card for a foul on Danny Cruz. His first had come in the 14th minute, also for a foul on Cruz.
The win keeps the Union in the Eastern Conference's final playoff spot. The loss is Chicago's third in a row.