Nikolay Zherdev and Scott Hartnell added goals, and Claude Giroux had three assists for the Flyers in the only regular-season rematch of last year's Stanley Cup Finals.
The 22-year-old Bobrovsky lost a bid for his first career shutout at 6:49 of the third period when Marian Hossa scored on a penalty shot. Philadelphia improved to a league-leading 69 points and is 9-2-0 in its last 11.
Defending Stanley Cup champion Chicago lost in regulation for the first time since Jan. 5 and had been on a 5-0-1 roll.
Chicago rookie Corey Crawford finished with 30 saves.
Bobrovsky was especially sharp in the first period before the Flyers took control of the game.
The Blackhawks had the better scoring chances in the up-tempo, scoreless first. Bobrovsky made several quick, close-in saves, including ones on Jonathan Toews and Tomas Kopecky.
As the period progressed, Chicago's skating and puck possession game became more dominant. But Carter opened the scoring 49 seconds into the second to cap a lengthy goalmouth scramble.
Crawford stopped Braydon Coburn's drive from the right point, but couldn't control the rebound. While Crawford was down in the crease, the Flyers managed several attempts that hit him or were blocked by Blackhawks skaters. Carter finally pushed the puck over the goal line to give the Flyers a 1-0 lead.
Philadelphia then tightened its play and coverage to slow down Chicago. Meanwhile, the Flyers generated several prime chances and ended up outshooting Chicago 19-9 in the frame.
Zherdev made it 2-0 at 2:28 of the third when he scored on a wraparound. He circled the net and tucked in a shot from the left side before Crawford could cover the post.
Carter scored again just under three minutes later to extend the Flyers' lead to 3-0. He tipped in Giroux's centering pass in midair from the edge of the crease to complete a three-on-two break.
Hossa was awarded his penalty shot after Coburn closed his hand on the puck during a goalmouth scrum. Hossa beat Bobrovksy between the legs with a wrist shot. He became the first Blackhawks player to score on a penalty shot in a home game since Troy Murray in 1987.
Hartnell completed the scoring with an empty-net goal with 52 seconds left.
Notes: The Flyers remain one of two NHL teams without a shutout. ... Philadelphia LW James Van Riemsdyk missed the game with a lower-body injury. ... Toews, Chicago's captain, was in the lineup. He sat out the end of the Blackhawks' 4-1 win at Detroit on Saturday after a collision in the third period. ... Sunday's game started at 11:30 a.m. and concluded just before the start of the NFC Championship game between the Bears and Packers at Soldier Field.