Coronato took a pass from Matvei Gridin during a 3-on-1 rush and snapped a shot from the slot to the blocker side past Dan Vladar.
Zayne Parekh, Zach Whitecloud and Joel Farabee scored for the Flames (8-9-1), who had lost two in a row (0-1-1). Yegor Sharangovich had two assists.
Devin Cooley made 31 saves in his first start since Oct. 28. He dressed as the backup on Friday (a 5-3 loss to the Anaheim Ducks) after missing the previous four games with a lower-body injury.
Denver Barkey, Noel Acciari and Owen Tippett scored for the Flyers (4-10-5), who have lost three straight (0-2-1). Sean Couturier had two assists, and Vladar made 22 saves.
Barkey scored to give Philadelphia a 1-0 lead at 12:46 of the first period, taking advantage of a 3-on-1 rush for the Flyers after Parekh fell in the neutral zone. Cooley made a pad save to stop Couturier’s initial shot, but the puck bounced out to the front of the left circle to Barkey, who snapped it in to extend his point streak to three games (two goals, one assist).
Parekh tied it 1-1 at 15:26. He took a pass at the right point from Yan Kuznetzov and skated into the left face-off circle before quickly pivoting and snapping a shot into the top right corner over Vladar’s glove.
Acciari scored his second goal in as many games at 2:16 of the second period to put the Flyers up 2-1, redirecting Nick Seeler’s point shot over Cooley’s left arm.
Whitecloud replied with his first goal of the season at 5:59 to pull the Flames into a 2-2 tie. Aydar Suniev kept the puck in at the blue line and passed it over to Whitecloud, whose wrist shot from the top of the left circle beat Vladar to the blocker side.
The Flyers went back up 3-2 with a power-play goal at 15:07 by Tippett, who picked up a rebound in the slot before turning and scoring on a wrist shot to the glove side.
Farabee scored on a short-handed breakaway at 8:27 of the third period to even the score 3-3. Farabee has found the back of the net in six straight home games (six goals).
