Staal broke a tie 9:34 into the third period, and Skinner had two goals and an assist as the Hurricanes rallied from a two-goal deficit and beat the Panthers 5-3 on Friday night.
"We'd like to get off to a better start," Skinner said. "I think we play better when we're a bit angry. After those first two goals we got a little bit angry, and that sparked us to play a better game."
It was the third time in five games against Florida that Carolina rallied from a two- or three-goal deficit.
The Hurricanes wiped out a 3-0, first-period hole to win 4-3 on Dec. 15 and came back from being down 3-1 down in the third period on Monday, before losing 4-3 in overtime.
"Up 2-0, we should have taken control," Florida defenseman Bryan Allen said. "Carolina does it time and time again against us."
Staal scored his 20th goal of the season after a turnover in the neutral zone. He skated in the Florida end and beat Tomas Vokoun to the glove side with a wrist shot.
Staal has scored at least 20 goals in six consecutive seasons, joining Kevin Dineen and Ron Francis as the only players in team history to do it.
"I tried to delay a little bit," Staal said of his goal. "I let a good wrister go and I think it went off their 'D' stick a little bit and caught Vokoun with a good shot over the glove."
Erik Cole added an insurance goal at 17:00 when he took Skinner's backhand pass in front of the net and fired a wrist shot past Vokoun. The teams then traded goals in the final minute.
Skinner, who came into the game leading NHL rookies with 28 points, scored his goals in the second period to help Carolina tie the game.
Cole also had two goals, including an empty-netter, and Tuomo Ruutu added three assists.
Justin Peters, making only his seventh start of the season, stopped 32 shots for Carolina, 4-0-2 in its last six games.
"I'm really happy for him," Hurricanes coach Paul Maurice said. "He hasn't played a lot. He kind of got shelled in his last game, and his numbers aren't great. This is a real important game for him because he earned the win."
Peters is 2-4-1, with both victories coming at Florida.
"That's just the way it goes," Peters said. "It's a fun barn to come in and play. I was just excited about the opportunity."
Marty Reasoner scored twice for the Panthers, 5-3-2 in their last 10 games. David Booth had the other Florida goal. Vokoun, who was pulled in the second period in his previous start on Wednesday, made 30 saves.
"We kind of got off our game," Reasoner said. "We had a good first period but then we let them back in the game again."
Skinner scored his first goal 1:46 into the period with a nifty move from the slot. After taking a pass from Ruutu, Skinner faked a shot before stickhandling around defenseman Dmitry Kulikov and beating Vokoun with a wrist shot.
Skinner was fortunate on his second goal. Patrick Dwyer's pass was deflected, bounced off Skinner's leg and off defenseman Dennis Wideman before floating over Vokoun's head.
"The second one was a bit of a lucky bounce," Skinner said. "You look back at times when things aren't going well and you get bounces like that. I tried to slow down to bat it out of the air and it tipped off my leg and sort of found a way in there."
Booth opened the scoring at 1:36 when he beat Peters between the legs with a wraparound. Reasoner made it 2-0 at 12:30 when he tipped in Wideman's slap shot from the point.
"We came out with the right attitude. We were prepared," Florida coach Pete DeBoer said. "The first period was fantastic. There wasn't any change of mindset or anything else. We just hit a little bit of a fatigue wall and started making some mental mistakes."
- Carolina is 6-1-4 in games tied after two periods.
- Carolina D Joni Pitkanen (upper body) and F Jussi Jokinen (lower body) both missed their fifth consecutive game.
- Florida LW Evgeny Dadonov returned after missing one game because of an ankle injury.
- Reasoner's goal was his first in nine games.
- Carolina recalled C Jon Matsumoto from Charlotte of the AHL and placed F Jiri Tlusty on the injured list, retroactive to Dec. 16.