Game 7 will be in Calgary on Sunday.
"We have a confident group," Stars forward Joe Pavelski said. "You know what? It's been a tight series. All the games have been tight, competitive, fun to play in, so yeah, I mean, we're a group, we expect to go in and win, and I'm sure they do, too. We expect the game to be similar as the first six."
Roope Hintz had a goal and an assist, and Jake Oettinger made 36 saves for the Stars, who are the first wild card from the West.
"I know we're not supposed to still be playing, we're supposed to be on a golf vacation right now, but that wasn't our intention going in," Dallas coach Rick Bowness said. "As I said right off the bat, we didn't get into the playoffs to be somebody else's steppingstone in the second round. Here we are going into a Game 7, and our guys deserve a lot of credit."
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Michael Stone had a goal and an assist, and Jacob Markstrom made 36 saves for the Flames, the No. 1 seed from the Pacific Division.
"It was a [heck] of a game, we just couldn't get the equalizer," Calgary coach Darryl Sutter said. "It takes a lot (to close out a series), guys are still learning how much it takes."
Hintz gave Dallas a 1-0 lead at 14:52 of the first period. Pavelski entered the zone and left a drop pass for Hintz, who shot five-hole from the left face-off dot.
"I think we need to do a better job of taking the middle away and limiting their speed through the neutral zone," Stone said. "We gave up too many chances against. They capitalized, and we didn't capitalize on ours."