Brad Marchand had two goals and three assists to extend his point streak to 10 games (seven goals, 13 assists), and David Pastrnak had five assists to extend his point streak to nine games (11 goals, 12 assists) and now leads the NHL with 23 points.
Marchand, Bergeron and Pastrnak have combined for 54 points (23 goals, 31 assists) in 11 games this season.
[WATCH: All Bruins vs. Rangers highlights]
"I think it's a combination, we're getting good bounces and [Pastrnak] and [Bergeron] are so dangerous all the time," Marchand said. "Right now, we're confident each night and we're just kind of rolling it over into the next game. Hopefully, it continues."
Charlie Coyle and Zdeno Chara each had a goal and an assist, and Jaroslav Halak made 25 saves for the Bruins (8-1-2), who have won three games in a row and are 5-0-2 in their past seven.
Video: Enterprise Hat Trick: Bergeron lifts Bruins
Micheal Haley, Pavel Buchnevich, Chris Kreider and Brady Skjei scored for the Rangers (3-5-1). Henrik Lundqvist allowed four goals on 31 shots through the second period. Alexandar Georgiev made nine saves in the third.
Center Mika Zibanejad, New York's leading scorer (11 points) who was playing in his 500th NHL game, didn't play after the first period because of an upper-body injury sustained on a hit from Bergeron with 2:47 left in the first. He is day to day, coach David Quinn said.
Quinn refused to pin the blame for the loss on the Zibanejad injury.
"I think part of being a professional athlete is handling adversity and understanding a consistent battle level gives you a chance to have success," Quinn said. "I just think we have guys that don't fully understand that. I think they think the game should be played a different way, that it should be a skilled game. Skill certainly is a huge component of this game, but if you have no battle in you, I don't care how skilled you are, you're not going to be productive.
"I mean, this game is all about what can you do when someone is trying to stop you from doing it. I don't care whether you're in the driveway, whether you're in practice, I don't care how pretty all these plays you can make, you've got to be able to make a play when someone is trying to stop you from doing it. And, in turn, you better try to stop someone else from making a play. We didn't have any of that tonight."
The Rangers took a 1-0 lead when Haley scored off a rebound at 10:19 of the first period.
Bergeron scored 11 seconds into the second period to tie the game 1-1. Pastrnak was tripped into Lundqvist, the puck stopped in front of the left post, and Bergeron put it in.
Video: BOS@NYR: Bergeron tucks home rebound to tie game
The goal was upheld by video review initiated by the Situation Room to determine if the puck entered the net legally.
"We just got beat on a 1-on-1, got beat to the net and panicked," Quinn said. "It just snowballed from there. That's really what happened."
Marchand scored 57 seconds later to give Boston a 2-1 lead at 1:08.
Video: BOS@NYR: Marchand beats Lundqvist with backhand shot
"Getting those quick goals to start the second got us going," Bergeron said.
Coyle made it 3-1 with his first goal of the season at 9:27, and Marchand scored again at 12:09 to extend the lead to 4-1.
Chara scored 43 seconds into the third period to make it 5-1.
Buchnevich made it 5-2 at 8:15.
Video: BOS@NYR: Buchnevich, DeAngelo combine for goal
Bergeron made it 6-2 at 11:39 with his second goal.
Kreider scored a power-play goal with 1:59 left to make it 6-3, and Skjei scored 21 seconds later to make it 6-4 with 1:38 remaining.
Bergeron finished the hat trick with an empty-net goal to make it 7-4 at 19:15.
They said it
"We weren't concerned at all [after the first period]. We did dominate that period. They had some shots on the power play, but other than that they didn't have much. Even their goal was a little lucky. So we knew if we continued to play the same way, we were going to break out, and we did." -- Bruins forward Brad Marchand
"We need to understand how hard we have to play every night. It's just not going to be enough. Some of it might be confidence, but we have to play very simple, very hard. It comes down to battles. That's how you win in this league. I felt like in the second period they did whatever they wanted to do. Maybe it was not the entire Boston team, it was more their top guys. They're one of the best lines in hockey and if you don't play them very hard, smart, they're going to expose you, and that's what they did. ... But it's more the battle level, it needs to come up." -- Rangers goalie Henrik Lundqvist
Need to know
Rangers forward Jesper Fast was a late scratch for personal reasons. Quinn said he wasn't certain if Fast would be available to play against the Tampa Bay Lightning on Tuesday. ... Bruins forward Par Lindholm left the game in the second period with an upper-body injury. ... Tony DeAngelo (two assists) became the first Rangers defenseman to have three straight multipoint games since Hockey Hall of Famer Brian Leetch in 1996-97.
Bruins: Host the San Jose Sharks on Tuesday (7 p.m. ET; NESN, NBCSCA, NHL.TV)
Rangers: Host the Tampa Bay Lightning on Tuesday (7:30 p.m. ET; NBCSN, NHL.TV)
Video: Bergeron scores hat trick as Bruins defeat Rangers