Since losing five straight, the Hurricanes have earned points in their last three games. They have two more remaining on a five-game homestand.
"I think it's all just coming together," Carolina coach Kirk Muller said. "We have had a couple of good, strong games lately and we are playing well."
Carolina was 0 for 3 on the power play, while Minnesota finished 0 of 4.
Neither team had enjoyed any success in shootouts this season. Minnesota lost its three previous tries, including its last game at Washington. Carolina's record in the tiebreaker fell to 0-3.
"We played a real solid game from start to finish," said Peters, who got his first career assist. "I just wished I could have gotten one of those shootout goals to give us a chance, but they made some real nice moves."
Pominville opened the scoring 3:33 into the first period on a breakaway for his 200th NHL goal.
The Hurricanes responded 1:20 later when Murphy, a second-year defenseman, took a shot from the right point that Harding couldn't stop.
Tlusty made up for a pair of penalties he took in the first period by scoring his third goal of the season. He slipped a shot underneath Harding's pads as he skated through the slot at 7:14 of the second period.
Fontaine tied it 4:08 later.
Minnesota D Ryan Suter extended his assist streak to four games and leads the Wild with 11 this season. ... Carolina RW Alexander Semin picked up his first assist since Oct. 28, giving him eight for the season.
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RALEIGH, NC - NOVEMBER 09: The Carolina Hurricanes warm up prior to their NHL game against the Minnesota Wild at...