Brayden Schenn scored for the Flyers (13-10-3), who won their season-high fourth straight game. Steve Mason made 26 saves.
Artemi Panarin scored for the Blackhawks (16-7-3). Scott Darling made 27 saves.
Darling started because Corey Crawford needed an appendectomy Saturday morning and will be out 2-3 weeks. Chicago signed Eric Semborski to an amateur tryout to be the backup goalie. Demborski, 23, played for the Temple University club hockey team, and also works as a coach and instructor for the Ed Snider Youth Hockey Foundation.
The Flyers trailed 1-0 early in the second period when Provorov's shot from above the left circle went off the stick of Blackhawks defenseman Trevor van Riemsdyk and past Darling at 3:02. Then at 3:33, his slap shot from inside the blue line beat Darling to give the Flyers a 2-1 lead.
"Score one goal in a game, that's a pretty good feeling," Provorov said. "And then score two in one shift, that's pretty unbelievable."
Schenn finished a give-and-go with Travis Konecny at 8:37 of the second to make it 3-1.
The Blackhawks thought they scored at 16:38 of the second when Richard Panik's shot from the side of the net hit off traffic in front, but Provorov gloved it out of the goal crease. Video review to check if the puck had crossed the goal line proved inconclusive.
"I came from the left corner and I saw the puck was rolling on [Mason's] shoulder," Provorov said. "I went down and rolled to the goal line, got there as quick as I could and swiped it out."
Provorov, 19, had one goal in his first 25 games but has played at least 20 minutes in eight straight games, including a Flyers-high 20:38 Saturday.
"Provorov stepped up in the second," Mason said. "You come in to a League at a young age, it's not easy and you've got to get your feet under you and we're starting to see that."
Panarin's goal at 3:44 of the first period gave the Blackhawks an early lead, but they were unable to build on it.
"I didn't mind most of the game," Blackhawks coach Joel Quenneville said. "There were stretches in our own end that coverage was off, especially with their defensemen coming down from their own end."