Dylan Strome scored two goals for Chicago (20-28-8), and Kevin Lankinen made 23 saves.
The Blackhawks are 0-15-1 since last winning a regular-season game in Philadelphia, on Nov. 9, 1996. They did win the Stanley Cup in Game 6 of the 2010 Final at Wells Fargo Center.
"I thought we played a pretty good game," Chicago defenseman Seth Jones said. "We had a lead on the road at a tough building to play in. Up 3-2, we were feeling pretty good about our game. The last two goals that we gave up were unforced errors on our part."
Brassard tied the game 3-3 at 3:09 of the third when his shot from the right side off the rush got through Lankinen.
It was Brassard's first goal since Nov. 20, and came after he and coach Mike Yeo met to discuss his poor play in a 5-4 loss to the Minnesota Wild on Thursday.
"That's what we were looking for, accountability," Yeo said. "It's one thing to say it but you've got to go out and do it."