Philadelphia, the Supporters Shield winners after finishing the regular season with the best record in the league, needed a penalty shoot-out to beat Chicago in the first game of their best-of-three series.
The Union had looked to be cruising towards a straightforward win against eighth-seeds Chicago after second-half goals from Indiana Vassilev and Milan Iloski eased them into a 2-0 lead with 15 minutes remaining.
But Chicago set up a nervy finish when left winger Jonathan Bamba pulled a goal back in the 84th minute.
Chicago's former Union defender Jack Elliott then silenced the home crowd in the third minute of stoppage time, uncorking a ferocious low shot from outside the area that flew into the bottom corner.
There was still time for Chicago to be reduced to 10 men moments later when substitute Sergio Oregel was shown a red card for his part in a melee with Philadelphia Kai Wagner, but the Fire held on for the penalty shoot-out.
Philadelphia held their nerve in the shoot-out, and Jesus Bueno slotted the winning kick after Chicago's Joel Waterman had blasted his penalty against the crossbar.
In the Western Conference, top seeds San Diego began their playoff campaign with a 2-1 victory over eighth-ranked Portland.
In Vancouver, the second-seeded Whitecaps swatted aside seventh-seeded FC Dallas 3-0 to take a 1-0 lead in their series.
The Whitecaps took the lead from a Daniel Rios header in the first half before former Germany and Bayern Munich star Thomas Muller doubled the lead from the penalty spot in the 60th minute. Kenji Cabrera made it 3-0 seven minutes from time.