Daniel Gadzag and Julián Carranza each had a goal and an assist for the Union (13-3-9, 48 points), who extended their home regular-season unbeaten streak to 18 matches (13-0-5). Andre Blake made six saves for Eastern Conference-leading Philadelphia.
Chris Mueller scored for the Fire (8-11-6, 30 points), which fell below the playoff line in the East. Chicago's Gabriel Slonina made three saves, including a diving stop against Mikeael Uhre in the ninth minute.
"I told the players after the game is that we have to put this one behind us," Fire head coach Ezra Hendrickson said. "We have had a good run of form and tonight we just didn't show up. When you don't show up in this league, especially against a team like that, first place in our conference, you know, you're going to pay."
Gazdag gathered Carranza's pass in the box and scored his 12th goal this season for a 1-0 Union lead in the 16th minute. Blake stopped a strike from Kacper Przybylko in the 27th minute to preserve Philadelphia's advantage.
Jack Elliott made it 2-0 in the 37th minute with his first goal this season.
The Fire pressed before halftime and had three corner kicks by Xherdan Shaqiri, all turned aside by the Union. Chicago continued to press after the break, and Mueller scored off a pass from Shaqiri to make it 2-1 in the 49th minute.
Carranza regained a two-goal lead for the Union in the 53rd minute when he chipped a shot over Slonina.
Burke, who entered as a substitute in the 72nd minute, scored in the 82nd minute for the 4-1 final.
Chicago's Gaston Gimenez was carried off on a stretcher by trainers in the 66th minute after a tackle by Elliott.
“He felt something in the hamstring, so it doesn't look good," Hendrickson said of Gimenez. "Obviously he couldn't finish out the game. That's a concern and we'll find out more tomorrow. It didn't look good.
"We're hoping to have (Carlos) Terán back next weekend. So if that happens, Terán slides back into his center back position, and Mauri comes back into the midfield. But if Terán is not ready, then we have (Javier Casas Jr.), we have (Fabian Herbers) and we have guys who can play in the midfield alongside Federico (Navarro).”
PHI - Gadzag (12) (Carranza 6) 16’
PHI - Elliott (1) 37’
CHI - Mueller (4) (Shaqiri 11, F. Navarro 3) 48’
PHI - Carranza (9) 53’
PHI - Burke (5) (Mbaizo 3, Gadzag 6) 82’
Stats Summary: PHI/CHI
Shots: 17 / 13
Shots on Goal: 7 / 7
Saves: 6 / 3
Passing Accuracy: 77.5% / 84.4%
Corners: 6 / 6
Fouls: 21 / 8
Offsides: 2 / 1
Possession: 43.7% / 56.3%
What's On Tap Next For the Fire?
The Fire return home to face reigning MLS Cup champion New York City FC next Sunday at SeatGeek Stadium. Kickoff is set for 5 p.m., with the match televised on WGN-TV.