Magee scored a goal in his third straight game and has eight goals in 10 games since coming to the Fire from the L.A. Galaxy.
Patrick Nyarko also added a goal and an assist for the Fire, who improved to 8-9-4.
Chicago is 2-0-1 in its past three games and got even for two previous losses to the Union this season.
Nyarko's goal in the ninth minute gave the Fire a 1-0 lead.
Sheanon Williams tied the game at 1 in the 60th minute when he finished a cross off a free kick by Sebastien Le Toux. It was Le Toux's league-best 10th assist.
The Union had been 2-0-1 in their previous three games. They fell to 5-3-4 at home and 9-7-7 overall.
Chicago improved to 4-5-1 against the Union.