Bergeron was chasing after a loose puck in the Flyers zone late in the first period when Jones closed in on him and drove his head into the boards with his forearm.
The 22-year-old crumpled to the ice and lay on his back motionless while the Bruins went after Jones, 26.
Martin Biron stopped 37 shots and Mike Richards had a short-handed goal for Philadelphia. Joffrey Lupol also scored.
Marco Sturm replied for Boston.
The win snapped the Flyers' two-game losing streak and handed the Bruins their first home loss of the season.
Medical personnel cut away Bergeron's jersey and shoulder pads as they worked on him, placing his neck in a brace.
They placed him on a board and then onto a stretcher, his legs taped together and his arms folded across his chest. There was little sign of movement. The game was delayed some 15 minutes as he was treated.
Bergeron was taken to Massachusetts General Hospital, where he was being treated by Bruins team physician Dr. Bertram Zarins. There was no immediate word on Bergeron's condition.
"Words can't express the way I feel right now," Jones said in a statement released by the team. "I am very apologetic for the hit and what I did. It wasn't intentional, it's something I have never done before, it is not part of my character.
"I'm extremely sorry, I hope he does OK and everything works out for him. I wish him nothing but the best in his recovery."
Jones was assessed a five-minute major and game misconduct at 16:07.
Jones' hit is the latest violent incident involving the Flyers this season.
Prospect Steve Downie was suspended 20 games after a hit to the head of Ottawa Senators forward Dean McAmmond in an exhibition contest. Then on Oct. 10 in Vancouver, Jesse Boulerice laid a vicious cross-check to the mouth of Canucks centre Ryan Kesler that resulted in a 25-game suspension.
After the Boulerice incident, the Flyers found themselves fighting off an emerging perception that they were a team full of out-of-control goons.
"I think we're in agreement that there's no place in the game for this anymore," general manager Paul Holmgren said Oct. 12. "I do think it was an isolated incident."
Added head coach John Stevens: "It's almost implied that's the direction we're going when it couldn't be further from the truth."