Bergeron scored his 19th goal, on the power play, for a 3-1 lead when he redirected Torey Krug's shot past a screened Georgiev at 15:11.
"The second of a back to back, sometimes when a team is coming at you, you have to weather the storm," Bergeron said. "We found our legs and got better as the period went on. Good second and bad third."
Zibanejad's 22nd goal at 17:45 of the first put the Rangers ahead 1-0 and extended his point streak to four games (five goals, four assists). Mats Zuccarello retrieved the puck from behind the net and fed Zibanejad at the point for a one-timer. It was Zibanejad's 10th goal in the past eight games.
"You have to remember the Bruins are a good team, a real good team," DeAngelo said. "They had a good push in the second. I thought we controlled the first and we came out and had a real strong third. It was important for us to get a big comeback win at home."