Ondrej Kase scored, and Jack Campbell made 30 saves for the Maple Leafs (9-5-1), who have won seven of eight games.
"We're playing hard and everybody was doing their job going back hard into the zone," Campbell said. "The defensemen were making great plays and the forwards were helping out and there were a lot of blocked shots again tonight. It was kind of a playoff feel. Calgary is a deep team with a lot of great structure and [they] don't give you too much. Their goalie played amazing tonight and really kept them in it, especially on a back-to-back for them."
Oliver Kylington scored, and Vladar made 35 saves for the Flames (7-3-4), who are 0-2-1 in their past three. They were coming off a 4-2 loss at the Montreal Canadiens on Thursday.
"I thought we played a really good game," Calgary coach Darryl Sutter said. "We have been playing really well, just haven't scored. I thought Dan was really solid. They've got a lot of high-octane shooters. The goalie has to make some good saves, which he did."
The Flames went ahead 1-0 at 4:55 of the third period when Kylington scored on a give-and-go with Johnny Gaudreau, shooting over Campbell's outstretched left pad.
"It was a nice goal, but at the end we didn't win," Kylington said. "For me, winning is the most important thing. I don't care if I score or get points, I just want to win games, and we didn't do it today."