Leafs goaltender Frederik Anderson was up to the task in the tilt, making 19 saves in the game, and denying several great chances by the Flames.
At the other end of the ice, Flames goalie Mike Smith played well for the home side, stopping 26 shots, including some highlight reel material.
"I don't think we did enough," admitted captain Mark Giordano. "They're a good team and they play with a lot of speed, but they do the little things. They chip the puck a lot. A few mistakes cost us this game. We didn't play that badly, but there were a few key moments in the game where they took advantage and got some big goals.
"If you score one goal, on most nights you're not going to have a chance to win. It's going to be pretty tough. We had our opportunities, but I thought they were better tonight."
With just over five minutes left in the first period, Tyler Bozak led a Leafs rush and with a man open in front of the net, he slid a perfect pass over to Mitch Marner, who was promptly denied by an amazing pad save from Smith.
The Maple Leafs took a 1-0 lead in the opening frame when defenceman Roman Polak's point shot deflected off of Flames defender Travis Hamonic and past Smith.
"The first one is going eight feet wide and it hits Harmonic and goes in," said Stone. "That being said, Smith made some really good saves to keep it scoreless until then."
Calgary's best scoring chance of the period came on a nice cross-crease saucer pass from Johnny Gaudreau that jumped just over the stick of Sean Monahan.