The Stars (30-26-5) have lost four of their past five games, including being shut out three times, and are tied with the Colorado Avalanche in points but hold the first wild card into the playoffs from the Western Conference, one point ahead of the Minnesota Wild. Ben Bishop made 28 saves in his first start since Feb. 4 because of an upper-body injury.
"I think we're trying, but we're not playing smart," Stars defenseman John Klingberg said. "We gave up two goals, and then we're chasing too much, not staying with our system and turning too many pucks over. It could have been 5-0 and, obviously, we're not that dangerous offensively either."
Wallmark gave the Hurricanes a 1-0 lead at 3:15 of the first period, scoring on a one-timer off a pass from Greg McKegg on a 2-on-1 after Warren Foegele's loft pass got past Stars defenseman Taylor Fedun.
"Give [Wallmark] credit, he had to play a lot of minutes and fill big shoes (in Jordan Staal's absence)," Brind'Amour said. "He did a great job for us. He did a good job and now it's good for him to not have that pressure that we had to put on."
Jamie Benn nearly tied it on a breakaway at 15:04, but his backhand shot hit the post.
Faulk scored on a 5-on-3 power play to give Carolina a 2-0 lead at 1:01 of the second period, beating Bishop blocker side on a wrist shot from the top of the right circle.
Dallas appeared to score at 19:11, but Blake Comeau was called for goalie interference.
"I had a couple body checks in the second period," McElhinney said. "Sometimes it helps to get you into the game. It was pretty quiet after that point. Those are certainly wake-up calls."