The Union, who began the night tied for first place with Toronto FC in the Eastern Conference, improved to 13-3-5 (44 points). They also moved to 8-0 at home this season.
Robert Beric scored the lone goal for the Fire, his eighth in 10 games. Chicago fell to 5-9-6 (21 points).
The Fire remain the only team in the league without a road victory.
The Fire controlled much of the possession in the first 15 minutes but had no real scoring opportunities.
Beric fired a right-footed shot just wide in the 22nd minute.
The Union went ahead 1-0 in the 28th minute when Przybylko scored on a penalty kick. The penalty was called two minutes earlier following a hand ball by Francisco Calvo in the box.
In the 36th minute, Calvo was sent off with a red card for a reckless tackle against Bedoya. The Fire played the rest of the game with 10 players.
Chicago still managed to tie the game in the 42nd minute when Beric headed a shot into the goal.
Philadelphia's Brenden Aaronson dribbled through a pair of defenders in the third minute of stoppage time but had his shot blocked.
The first 15 minutes of the second half were rather chippy with multiple fouls on both teams.
In the 76th minute, the Fire nearly equalized when Beric headed a free kick barely wide of the goal. On that play, Philadelphia goalkeeper Andre Blake (three saves) looked to bang his right hand against the post. Blake stayed down for several minutes but remained in the game until the 89th minute when he was replaced by Joe Bendik.
Bendik, who made his debut for the Union, survived eight minutes of stoppage time.