Markstrom led the NHL with nine shutouts in the regular season. It was his second career postseason shutout and first since Aug. 6, 2020, when he made 27 saves for the Vancouver Canucks in a 3-0 victory against the Minnesota Wild in Game 3 of the Stanley Cup Qualifiers.
"He was solid," Calgary defenseman Erik Gudbranson said of Markstrom. "He was really solid. There were moments in the game when he needed to be sticky and he was sticky and got a whistle for us. I mean, we trust him. He's a great goaltender."
Elias Lindholm scored the only goal of the game for the Flames, the No. 1 seed in the Pacific Division.
Game 2 will be played here Thursday.
RELATED: [Complete Flames vs. Stars series coverage]
"I think it was an emotional game, a tight checking game, but it's just one game," Calgary forward Blake Coleman said. "I said it going into the playoffs, it's going to be a marathon, not a sprint. We have to find ways to learn from our mistakes in these games and then find ways to build on things we did well and obviously that will be what we work on tomorrow. I'm sure the staff will have us prepared and ready to go for Game 2.
"But I think that's the beauty of this team; we can play whatever way you want. We can rough it up a little bit, we can make plays, we can defend, we have great goaltending. Whatever the game calls for, we can meet that challenge."
Jake Oettinger made 25 saves in his first NHL playoff start for the Stars, the first wild card in the West.
"You can't get too high or too low in the playoffs here," Oettinger said. "I think we feel that we didn't play our best game and we lost 1-0, so I think we should feel confident about that. I know the guys are going to respond and play even better the next game."