The goaltenders were the story of the game through much of the first two periods.
The Flames forced Flyers netminder Samuel Ersson into a couple of early glove saves including on a chance from Gilbert just past the three-minute mark.
The Calgary defender stepped around a Flyer before wiring a shot into Ersson’s glove from the left circle.
A minute later, Markstrom was forced into an early stop when Philadelphia blueliner Travis Sanheim snuck in for a breakaway; the Flames puck-stopper blockered aside Sanheim’s effort from the low slot.
The Flyers opened the scoring just shy of the 10-minute mark, though, defenceman Rasmus Ristolainen finding his first goal of the season after he jumped up and converted on a cross-zone feed from the right circle.
At the other end of the ice, Ersson was forced into his most challenging stop of the period with just under seven minutes remaining in the opening frame. Martin Pospisil fizzed a hard pass from left to right across the Flyers zone onto the tape of Rasmus Andersson, who then weaved his way into the low slot before unleashing a backhand chance that was a right toe away from entering the net.
The Flames kept pressing, but the Philly goalkeeper stopped all 12 shots that came his way, denying Jonathan Huberdeau on a pair of notable opportunities including a redirect attempt from just outside the blue paint.
The locals had a glorious opportunity to even the score two minutes into the middle stanza.
Backlund sifted a puck across from left to right to Elias Lindholm on a short-handed odd-man rush, but Lindholm’s snapshot was deflected away by a desperate Ersson, who thrust his left arm out to get just enough of the puck to direct it past his post.
The goaltending duel continued through the bulk of the period, Markstrom stating his case with just under six minutes left with a cool series of stops off Cam Atkinson and Morgan Frost after Atkinson tried his luck from the right flank.
The homeside found its long-awaited equalizer at the 18:21 mark. Gilbert chipped a puck into the left corner to Andrew Mangiapane, who froze a Philadelphia defenceman before spotting Backlund in the slot.
The Flames captain slipped away from a defender into space, then one-timed his eighth goal of the season over Ersson’s left shoulder.