Dan Vladar made 32 saves for the Flames (4-7-2), who had won two in a row and trailed 4-1 early in the second period. Yegor Sharangovich scored in the shootout.
“That resiliency. I mean, that's always good to see,” Calgary forward Nazem Kadri said. “Character, effort, that’s always a positive especially if there's a takeaway from today's game, just being able to secure a point and get out of here with at least one or two points."
Jarnkrok gave the Maple Leafs a 2-1 lead at 8:18 of the first period when he took a pass from Domi and backhanded a shot in the slot.
Nylander pushed the lead to 3-1 with a short-handed goal at 1:06 of the second period. He stole the puck from Noah Hanifin at the red line, skated into the zone on a 2-on-1 with Noah Gregor and shot from the top of the left face-off circle.
“When you look at the first three goals, they were gifts that we gave them and then we took on some water for sure in the third period,” Flames coach Ryan Huska said. “The half-full part is that we battled back, we were down 4-1 and we found a way to get a point.”
Woll kept it a two-goal game by stopping Martin Pospisil on a breakaway at 2:51.
Tavares made it 4-1 at 4:45 when he one-timed a no-look backhand pass in the slot from Nylander, who was behind the net.
“I told him it was an unbelievable feed,” Tavares said. “Just great instincts and using his body to protect the puck and making the play all in kind of one sequence there, one motion. He put it in a great spot for me and gave me ample time to pick my spot.”