Nylander cut into the slot from the left wing and shot past David Rittich to give Toronto the win.
"I just got some speed and got a nice pass from [Auston Matthews] and was able to take it to the net. It was nice to be able to score finally," Nylander said.
Michael Hutchinson made 21 saves for the Maple Leafs (15-4-2), who tied the game with 1:28 left in the third period.
"It's always fun [to be in a low-scoring game], but as the game goes on, especially when you're feeling like you're on top of your game, you just become more at ease as the game goes on," Hutchinson said. "It doesn't matter if you're up a goal or down a goal, the longer the game goes, the more comfortable you feel and you're kind of just in a zone."
Andrew Mangiapane scored with 3:27 left in the third, and David Rittich made 37 saves for the Flames (9-9-2), who defeated the Maple Leafs 3-0 on Monday.
"When we needed a big save, [Rittich] made it," Calgary coach Geoff Ward said. "He's coming off two strong performances. He's a guy who once he gets momentum; he's someone who can maintain it. We'll take the three out of four points out of Toronto. I thought there were a lot of positives. We'll take it."
Nylander jammed in a loose puck during a scramble in the slot at 18:32 to tie it 1-1. It was Toronto's first goal in 124:56 and ended Rittich's shutout streak at 137:35.
"It was a scramble in front of the net," Rittich said. "I saw that puck, I tried to cover it and he smacked it in just in front of my glove. I'm going to be OK tomorrow. I'm just not feeling very awesome right now because we lost 2-1 in overtime. I'm there to help guys out. It's my job. I'm doing what I love. I'm playing hockey. What else can I say, what else can I do but save the puck."