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.