Chicago started brightly and broke the deadlock after nine minutes, benefiting from a huge slick of luck in the early stages to claim an early advantage.
A Fire free kick lofted into the penalty area bounced off United defender Nick DeLeon and looped into the top corner for a bizarre own goal.
Just before the break United struck the woodwork as Dwayne De Rosario's effort from distance came crashing back off the crossbar.
Wasteful finishing continued in the second half as the match remained finely poised going into the closing stages.
Five minutes from time Chicago doubled their advantage to seal the precious three points through Magee, who sent a shot safely into the bottom left corner from close range.