Mikael Backlund shot over Jarry's glove in the seventh round of the shootout before Markstrom stopped Brock McGinn for the win.
"I just checked a little bit before, kind of where he's been letting goals in," Backlund said. "I tried the move in practice and scored on 'Marky,' so I figured if I can score on Marky I can do it on this guy, too.
"You're always ready to get the call to go, not that I'm expecting with my record, 0-for-7 before today, I wasn't expecting to get picked early, but when I heard my name, I got excited."
Johnny Gaudreau had two chances to win it for the Flames in overtime. He hit the crossbar at 1:16, and Jarry stopped him with his glove from the edge of the crease at 3:54.
"[Jarry has] played a lot of good ones, but he certainly played well tonight," Pittsburgh coach Mike Sullivan said. "He helped us earn an important point."
Lucic put Calgary ahead 1-0 at 9:44 of the second period. Shortly after Markstrom made a shoulder save on a redirection from Jason Zucker, Lucic skated into the left circle on a rush and beat Jarry five-hole.