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.
NOTES: 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.