Tlusty scored two goals, giving him a career-high 19, and the Hurricanes ended a seven-game losing streak with a 4-2 victory over the Bruins on Saturday.
The go-ahead goal came from Joe Corvo on a power play at 9:36 of the third.
The win was Carolina's first in the month of April and the Hurricanes also ended an eight-game losing streak at home.
"I'm happy for the guys," Carolina coach Kirk Muller said. "They've been playing like that for a while. Tonight they stuck with it and played an intense, energized game against a good hockey club. They played the right way and finally got some reward for it."
Jeff Skinner added a first-period power-play goal, the first time this season Boston had allowed two power-play goals in a game.
Peters' most impressive stop was a glove save on Jaromir Jagr during a 5-on-3 power play midway through the second.
"I wanted to put forth a great effort for the boys because of how hard they've been working and how great the atmosphere has been in here," Peters said. "It was nice to get a result. Jagr is an unbelievable player and it's an honor just to play on the same ice surface as him."
"We had some brain cramps out there tonight," Boston coach Claude Julien said. "The mistakes we made tonight were not helpful -- two power-play goals. Those are things we're dealing with right now."
The teams were tied 1-1 after a wild first period that had three fights.
Boston's Shawn Thornton tangled with Kevin Westgarth at 14:14, while Jay Harrison fought Bruins defenseman Zdeno Chara at 18:41. Carolina's Nicolas Blanchard, in just his second NHL game, dropped the gloves with Gregory Campbell at 19:32.
Lucic opened the scoring at 6:07 of the first, scoring his sixth goal on a deflection. Jagr had an assist for his 1,686th career point.
Skinner tied it on a power play at 19:24, taking a pass from Alexander Semin -- who finished with two assists -- and beating Rask from behind stick-side.
Tlusty gave Carolina a 2-1 lead at 14:04 of the second, receiving Eric Staal's pass from behind the net in the right circle and lifting it over Rask's right shoulder.
"Those guys who fought did a great job," Tlusty said. "Westy is a tough guy and Thornton is a tough guy, too. Blanch had a hell of a fight. And Harry jumping in on Chara is something else -- Chara is one of the biggest guys in the NHL."
The Bruins tied it 2-2 at 17:57 when Andrew Ference took the puck from Semin at the red line and passed to Seguin for a breakaway.
Corvo, who played for Boston last season, put Carolina ahead on the power play at 9:36 of the third when he received Marc-Andre Bergeron's pass on the left point and beat Rask over the right shoulder.
"There weren't many mistakes made out there," Corvo said. "Everybody did his job tonight and we got the good result. It's always nice to score and beat your old team."
Tlusty added an empty-net goal with 28.1 seconds left.
Boston will host Ottawa on Monday night while Carolina will visit Ottawa on Tuesday night. ... Boston C Patrice Bergeron, out since a concussion on April 2 against Ottawa, was back at full speed for the morning skate but did not dress, while C Brad Marchand remained out with his concussion suffered at New Jersey. Bruins D Dougie Hamilton was a healthy scratch for the second straight game. ... Carolina D Joni Pitkanen (five games, heel), C Tim Brent (two games, lower body), LW Drayson Bowman (two games, lower body) and RW Tim Wallace (first game, upper body) were scratches.