Lindholm's goal came after Markstrom stopped three Chicago breakaways earlier in the game. He made a toe save on Boris Katchouk's attempt in alone 2:19 into the first period, and got a pad on Lukas Reichel's deke at 9:10.
"Obviously you want to put on a better performance for your goalie, but he was dialed in tonight and he played an outstanding game," Flames defenseman Rasmus Andersson said. "Sometimes you need your goalie to steal a game and today was a perfect example of that."
Katchouk missed the net on a short-handed breakaway 3:36 into the second, and Markstrom made a glove stop on Philipp Kurashev's breakaway at 5:47.
"I know we've had some games where we've had maybe more chances and more shots than the other team, but maybe not the quality,” Blackhawks coach Luke Richardson said. “But tonight, I think we had the quality as well. I don't know if I've ever seen six breakaways in a game and zero on the score clock.
"It's frustrating, but I told the guys we've got to keep playing like that and they're going to drop, and we'll start getting healthier and get some more help in that department. We're playing the right way. We're proud of how we're playing, but it's still the NHL and we've got to find results somehow."
Markstrom stopped Kurashev's wrist shot with six seconds remaining before making a right-pad save on Jason Dickinson's rebound attempt with four seconds left to preserve the victory.
"I felt good," Markstrom said. "I thought the third period was a really good period. They didn't have much at all and we closed out the game, and that's what you need to do in a one-goal game, so it was good."
NOTES: Markstrom became the fourth Swedish-born goaltender in NHL history to record at least 20 shutouts alongside Henrik Lundqvist (64), Tommy Salo (37) and Johan Hedberg (22). … Chicago has been shut out in four of its past six games. ... Lindholm surpassed Eric Vail for eighth place on the Flames all-time game-winning goal list with 30. … Calgary defenseman MacKenzie Weegar’s three-game goal streak ended.