Andrew Mangiapane and Elias Lindholm scored, and David Rittich made 21 saves for the Flames (3-3-1), who had lost two games in a row.
"We've got a lot of expectations, obviously, from last year," Frolik said of finishing with the best record in the Western Conference. "I think last year, the first month we were kind of .500, and then we took off. The start could be better, but the last two games are pretty good for us."
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Matt Niskanen scored, and Brian Elliott made 35 saves in his first game of the season for the Flyers (2-1-1), who are 0-1-1 to begin their three-game Western Canada road trip that concludes against the Edmonton Oilers on Wednesday.
"We don't have to chew on this one very long. That's good," Niskanen said. "That's the good thing about back-to-backs. Nobody likes them, but if you lose that first one, you get to go after it again the next night. You don't have to think about it too long."
Frolik gave the Flames a 1-0 lead 1:35 into the game when he knocked down defenseman Justin Braun's clearing attempt and scored from the slot.
"Eight hundred, it's a special number," Frolik said. "I was definitely excited, for sure. It couldn't have gone better to score on the second shift. It gets you going too, right?"
Calgary's Sean Monahan scored with six seconds remaining in the first, but the goal was overturned after video review showed he kicked the puck into the net.
Mangiapane made it 2-0 at 14:15 of the second when his shot from the high slot went in off defenseman Travis Sanheim. It was the first goal for the Flames from a bottom-six forward this season.