Skinner scored two goals, Cam Ward made 36 saves in his 199th NHL win, and Carolina beat the Lightning 4-2 on Saturday night.
"[Tied] on the road going to the third, those are big games, especially down the stretch," Skinner said. "Ward was huge for us. The whole team contributed."
Skinner gave Carolina a 3-2 lead when he skated around the net and scored from a tough angle at 6:36 of the third period.
Skinner has eight goals and 11 points in 10 games against Tampa Bay.
"I saw that ... funny how it works," Hurricanes coach Kirk Muller said. "Individuals have certain teams they seem to have success with, but he does it with a huge goal for us tonight. That's a goal-scorer goal there."
Chad LaRose added an empty-netter, giving him a goal in three straight games.
Ward stopped all 18 shots he faced in the second period. He made two strong saves on NHL goals leader Steven Stamkos, including a spinning shot by the center from the low left circle.
"Their goalie played great," Tampa Bay coach Guy Boucher said.
Tampa Bay dropped five points behind eighth-place Washington in the Eastern Conference playoff race. Carolina trails the Capitals by seven points.
"We're quietly sneaking up on teams," Muller said. "We're putting points together. We're playing some good road hockey right now. Really, we're doing it as a team."
The Hurricanes took a 2-1 lead 12:29 in when Skinner beat rookie goalie Dustin Tokarskiwith a nifty redirection from just outside the crease off a pass from Jokinen.
Thompson stopped a 15-game point drought with a goal that pulled Tampa Bay even at 2 with 2:46 left in the first.
Malone put the Lightning up 1-0 just 1:20 in with a rebound goal from the slot.
Tampa Bay came out strong after the opening faceoff, getting three shots on Ward in the first minute.
"We can't push more than we pushed today," Boucher said. "Our guys had no more juice at the end. They gave everything they had. Our players were up for the challenge, it just didn't turn our way."
Carolina took advantage of an interference penalty on Lightning right wing Tim Wallace when Spacek tied it 1-1 with a power-play goal at 3:46.
Tokarski, recalled from Norfolk of the AHL on March 7 after starting goalie Mathieu Garon was sidelined by a groin injury, started for the second consecutive game. He made 22 saves, including an in-close stop on a late second-period shot by LaRose.
Skinner, LaRose and Jokinen all finished at plus-3 for the game.
- Carolina C Eric Staal played almost 18 minutes despite being ill.
- Hurricanes C Jiri Tlusty left with an undisclosed upper body injury.
- Tampa Bay RW Teddy Purcell had his career-high, 11-game point streak (15 assists, 22 points) end.
- Carolina RW Tuomo Ruutu was in the lineup after missing 10 games with an upper body injury.
- Malone has three goals and six points during a six-game point streak.
- Spacek has goals in consecutive games after scoring just one in the previous nine games.