Victor Hedman had three assists, and Steven Stamkos had a goal and two assists for the Lightning (58-13-4), who have won seven straight games. Tampa Bay has clinched the Presidents' Trophy, Eastern Conference and Atlantic Division.
The Lightning scored four unanswered goals in the third period.
[WATCH: All Lightning vs. Hurricanes highlights]
"I think guys worked hard, we skated for our chances and we were able to cash in," Tampa Bay center Brayden Point said. "It was just a better effort in the third."
Jordan Staal had a goal and an assist for the fourth-place Hurricanes (40-26-7), who trail the New York Islanders and Pittsburgh Penguins by four points for second in the Metropolitan. Pittsburgh defeated the Nashville Predators 2-1 in a shootout on Thursday, and the Islanders lost 4-0 at the Montreal Canadiens.
Video: TBL@CAR: Cirelli puts in Stamkos' backhand pass
Carolina leads Montreal by two points for the first wild card into the Stanley Cup Playoffs from the Eastern Conference.
"We [gave] it away and it's unacceptable," Hurricanes captain Justin Williams said. "They had an emotional game (a 5-4 overtime win at the Washington Capitals) last night. We should have been the ones in the third period to have the jump and push them out, but we didn't. They came back and they do what they do, they win games."
Anthony Cirelli took a backhand pass from Stamkos and held off Teuvo Teravainen to finish at the net and tie it 3-3 at 3:35 of the third.
Forward Ryan Callahan redirected Hedman's shot at the top of the crease to put the Lightning up 4-3 at 10:09. Callahan, who turned 34 on Thursday, had been scratched for the previous five games.
Video: TBL@CAR: Callahan deflects in go-ahead goal
"It felt really good," Callahan said. "Anytime you get in the lineup, you want to contribute any way you can. It was a pretty big goal at that point in the game. Obviously really excited it went in."
Lightning coach Jon Cooper said, "[Callahan's] still got plenty left. He works at his game, keeps himself in unreal shape, and he's a gamer. We needed that from him, it's great."
Point's power-play goal made it 5-3 at 16:36. Ryan McDonagh scored into an empty net with 1:05 left to make it 6-3.
"What I'm most proud of is how we played in the third, down a goal," Cooper said. "Pretty gritty effort, especially playing against a pretty desperate team that's trying to fight for the playoffs."
Louis Domingue made 25 saves for Tampa Bay.
Video: TBL@CAR: Point wires home PPG off Stamkos' feed
The Lightning took a 1-0 lead with a power-play goal at 3:20 of the first period. Hedman passed to Stamkos, who scored off the far post from the left face-off dot. Hedman extended his point streak to seven games (10 points; two goals, eight assists).
The Hurricanes tied it 1-1 on Nino Niederreiter's shot from the left hash marks at 9:51.
Dougie Hamilton scored on a long rebound to put Carolina ahead 2-1 at 11:32.
Tyler Johnson tied it 2-2 for the Lightning on a rebound with 26 seconds left in the period.
"They make plays, they're big and strong," Cirelli said. "We knew we were going to have to battle for a full 60 minutes. They obviously didn't go away, and we had some pushback."
Staal gave Carolina a 3-2 lead at 6:34 of the second period. He took a stretch pass from Teravainen and faked to the backhand before scoring at the top of the crease.
Staal had returned from a collision with Yanni Gourde late in the first period. Gourde was assessed a match penalty for an illegal check to the head.
Curtis McElhinney made 26 saves for Carolina.
"There were a few things that we weren't quite engaged fully (on)," Staal said. "Obviously they have the talent to burn you if you take the foot off the gas a bit."
They said it
"I think it's just our composure, our demeanor. Everybody talks about it in the media, the season we're having. But very rarely do you hear us mention it in here. It's always (about) trying to build our game. We know the real season starts in two weeks, and that's what we're focused on. It's what happens in the playoffs that matters." -- Lightning forward Ryan Callahan
"If we are going to play a team that good, everybody has to be dialed right in. We took breaths on a couple of goals, and that's inexcusable. Guys tapping in plays on the back door, that can't happen. We worked hard and had some opportunities, but (it's) not good enough against a team like that." -- Hurricanes coach Rod Brind'Amour
Need to know
Cooper got his 300th NHL win in his 500th game in the League. … Tampa Bay is 21-2-0 against the Metropolitan Division. … Point and McDonagh each had a goal and an assist, and J.T. Miller had two assists for the Lightning. … Hurricanes defenseman Brett Pesce got an assist on Staal's goal, setting an NHL career high with 19. … Carolina defenseman Jaccob Slavin played his 300th NHL game.
Lightning: At the St. Louis Blues on Saturday (8 p.m. ET; FS-MW, SUN, NHL.TV)
Hurricanes: Host the Minnesota Wild on Saturday (7 p.m. ET; FS-CR, FS-N, FS-WI, NHL.TV)
Video: Kucherov gets 120th point as Cooper reaches 300 wins