Rookie Joel Farabee got his first NHL point with an assist on Hayes' goal.
Brandon Saad scored, and Robin Lehner made 19 saves in his second straight start for the Blackhawks (2-4-2), who have lost three straight and went 2-3-2 on their seven-game homestand.
"We all have to get better," Lehner said. "I have to get better too. On the third goal, the breakaway, it would have been nice to have come up with a big save, and it would be 2-1 and who knows? But you don't get rewarded if you don't do the right things. I think it was an honest, well-deserved result today."
Lindblom gave the Flyers a 1-0 lead at 13:05 of the first period, scoring off a pass from Travis Konecny on a 2-on-1.
Saad cut the Philadelphia lead to 2-1 one minute into the third period when he scored on a breakaway.
"I think it just starts with turnovers," Saad said. "When we don't manage the puck, teams get momentum going the other way. Gave up way too many chances, odd-man rushes, breakaways tonight."
Hayes beat defenseman Brent Seabrook to the puck in the neutral zone and scored on a breakaway to make it 3-1 at 5:03.
"I think we've been practicing and harping on playing good team defense, not giving up goals, and I think [Flyers coach Alain Vigneault] has tried a system that we've all kind of bought into, and sometimes the pucks go in, sometimes they don't. But if you stick to the structure, you should be rewarded."
Van Riemsdyk blocked Erik Gustafsson's outlet pass and scored on a short breakaway to make it 4-1 at 16:44.
Hayes scored at 6:09 of the first period, but Chicago coach Jeremy Colliton challenged, and the goal was overturned after video review showed Hayes was offside at 6:06.
Farabee scored at 7:06 of the third, but Colliton challenged, and the goal was overturned after video review showed Hayes did not tag up at the blue line before the puck entered the Blackhawks zone at 7:01.