The shutout was Markstrom's second in his past three starts and 10th in 304 NHL starts. He has allowed one goal on 107 shots since Anaheim Ducks defenseman Jamie Drysdale scored against him in overtime Oct. 18 in a 3-2 loss at home.
Johnny Gaudreau had a goal and an assist for the Flames (5-1-1), who outscored their opponents 21-7 and never trailed on the trip.
"First of all, we have a long flight. It always [stinks] to travel after a loss," Markstrom said. "Then to end the trip on a good note, it's a great road trip instead of just a good one. I thought that was really important. That's a big win and something to build on."
Casey DeSmith made 31 saves for the Penguins (3-2-2), who have been outscored 9-1 the past two games after starting the season on a five-game point streak.
"[Markstrom] was really good tonight," Pittsburgh coach Mike Sullivan said. "You have to give him credit. He made a lot of big saves. We had a number of high-quality chances throughout the course of the game that we couldn't convert. … When you play goalies that are top-tier goalies, you have to make it hard on them."
Gaudreau put Calgary ahead 1-0 with his first goal of the season at 7:22 of the first period. After tipping a loose puck past Pittsburgh defenseman John Marino, Gaudreau carried it through the neutral zone to the left face-off circle for a wrist shot to the far side.
Gaudreau has 10 points (nine assists) during a six-game point streak.
"He's had a lot of really good opportunities every game this road trip," Flames coach Darryl Sutter said. "A player like that, it's going to [start going in] if he keeps getting them. He has a shot mentality, and he's taking those shots."