Oettinger, who had one shutout in the regular season and has two in his NHL career, has made 49 consecutive saves. He has not allowed a goal in 114:59, dating back to the first period of Game 1, a 1-0 loss on Tuesday.
"He's very calm, he's very confident," Dallas coach Rick Bowness said. "We're putting a rookie in a tough situation and we don't know how he's going to react until we give him that opportunity to play in the playoffs. We're very confident with him, clearly, but he's handled it very well. He's very confident and we love his poise in the net."
Joe Pavelski scored for the Stars, the first wild card in the West.
"I thought we made it too easy on them in the first game," Dallas captain Jamie Benn said. "We were better tonight. They're going to have their pushes and their good shifts and we handled them well and found a way to just dig in and get it done."
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Jacob Markstrom made 21 saves for the Flames, the No. 1 seed in the Pacific Division.
"It's playoff hockey," Calgary forward Tyler Toffoli said. "It's not easy to score goals in the first place, let alone playing a team like this who plays extremely defensive. We've got to find a way and kind of dig deep. Our goal was to go into Dallas and win two games anyways. It doesn't really change our mindset, I don't think. We have to go there and be prepared to play in Game 3 and just try to take control of the series again."
The best-of-7 series is tied 1-1. Game 3 is in Dallas on Saturday.
Pavelski put the Stars up 1-0 at 7:47 of the first period when he tipped Jason Robertson's wrist shot after a Calgary turnover in their own zone.
Pavelski, who didn't register a shot in Game 1, became the oldest skater to score a playoff goal for the Stars since Mike Modano (37 years, 342 days) in Game 4 of the 2008 Conference Finals. Pavelski is 37 years, 298 days old.
"Felt good," said Pavelski, who has the most goals scored in an NHL postseason by a United States-born player with 62. "You score in the playoffs it's always nice. Nice to get the lead, all those parts. Yeah, get that one and move on."