Quinn Sullivan added his first career MLS goal on a sensational bicycle kick that tied it at 1-1 in the 28th minute and Cory Burke took the team lead with his fourth goal to give the Union a 2-1 lead in first-half stoppage time.
The Union extended their unbeaten run to eight matches despite conceding three goals for the first time since March 8, 2020 at Los Angeles FC before last season was halted due to the pandemic.
Alvaro Medran contributed his first assists of the season on Chicago's second and third goals on a night in which the Fire nearly doubled their season total to seven goals.
Chicago also took the lead through an early own goal off Philadelphia defender Jakob Glesnes.
Przybylko nearly scored his fourth goal of the season to tie with Blake on the sequence that led to Philadelphia's equalizer.
After tangling with Chicago defender Fabian Herbers, the Union attacker reached the ball down the right, cut into the penalty area and unleashed a shot that required a diving stop from Bobby Shuttleworth.
But the ball went only as far as the shoulder of a retreating Sekulic, then bounded across the goal line to tie the match for the third time in the 79th minute.
Both sides had chances to win it late, but the best fell to Philadelphia's Jamiro Monteiro, whose drive was saved brilliantly by Shuttleworth low to his right.
Medran's first two assists of the season came only minutes apart.
In the 56th minute, he served a long, diagonal free kick toward the right side of the penalty area, where Sekulic met it unmarked and headed it past Philadelphia's Andre Blake from close range.
Then he curled a 67th-minute corner kick from the right toward the penalty spot. Burke couldn't quite reach it for a defensive clearance and it fell to Pineda, who side-footed a first-touch finish beyond Blake's dive and inside the right post.