Zach Hyman had a goal and an assist to extend his point streak to six games, and John Tavares had two assists for the Maple Leafs (28-11-4), who were coming off a 4-2 loss at the Montreal Canadiens on Monday that ended a six-game winning streak.
Rittich made 25 saves in his Toronto debut.
"It was a tough one, right. I played against my old team where I was for four years," he said. "I've got some life friends there. It was a tough one, and the even worse thing is we lost in overtime. It's great to be in Toronto though, beautiful city, great guys. It's a bunch of beauties here, so it's great."
Maple Leafs coach Sheldon Keefe said, "I thought he looked really good in the net. I'm sure it's a difficult night for him. The emotions are part of it, but then the actual game play is another thing. The colors of the jerseys and the different people on the ice, you're used to being on the other side, that can be difficult. But I thought he looked good in the net, he looked confident, he made some good saves for us; I don't think he had a chance on any of the goals. It was a good debut for him."
Lindholm gave Calgary a 2-1 lead 34 seconds into the second period when he one-timed a pass from Matthew Tkachuk in the slot on the power play.
Alex Kerfoot tied it 2-2 at 6:17 of the third period when he scored from the slot after a pass from Tavares from behind the net.