Connor Bedard scored his 30th goal of the season for Chicago (27-32-13). Spencer Knight made 37 saves. The Blackhawks are 2-2-2 in their past six games.
"We made a couple tough errors that end up in the net, and so then it's a grind," Chicago coach Jeff Blashill said. "Now you're fighting momentum on the road. I thought we clawed our way back a little bit and then made another couple tough errors, and now a real uphill battle. I just thought collectively, we didn't have enough guys close to their best."
Bump gave the Flyers a 1-0 lead at 48 seconds of the first period. Knight gave the puck away behind his net, and Dvorak passed in front to Bump, who scored into an open net.
The rookie forward, playing his 10th game, had an assist on Cates' goal in the second period for his first multipoint NHL game.
"I think it's kind of been a little bit of a roller coaster," said Bump, who made his NHL debut March 7. "I've definitely had some tough games, but I've definitely also had some good games too. I think right now for me, it's just kind of coming each game, bringing my best game, and don't worry about anything else."
Bump also matched his season best with four shots on goal, which is what coach Rick Tocchet has wanted from him.
"There's a play where he came into the interior and shot it, I love that play," Tocchet said. "It was a (heck) of a shot, instead of deferring. I told him on the bench, do that every time. ... He's got that lethal shot so we're going to keep developing him so he can continue doing that for us."
Couturier made it 2-0 at 2:33. Luke Glendening intercepted Andre Burakovsky's backhand pass off the boards deep in the Chicago zone, threw the puck at the net and Couturier redirected it past Knight.
Barkey put the Flyers ahead 3-0 at 5:14 of the second period when he got to the front of the net and knocked in the rebound of a Trevor Zegras shot.
Bedard made it 3-1 at 11:11. Anton Frondell made a backhand pass from below the goal line that went through the crease to a charging Bedard, who one-timed it past Ersson from the right side.
"I haven't really thought about it at this point," Bedard said of reaching 30 goals for the first time in his three NHL seasons. "When you're in a game like that and you're down and you score one, it's obviously more just hoping that it creates a little momentum. It's not something you think about as much, but obviously, anything positive, so just kind of try to keep put myself in positions to get chances."