Boston's top line of Brad Marchand (goal, assist), David Pastrnak (two assists) and Patrice Bergeron (goal) combined for five points. Tuukka Rask made 28 saves.
"It's just too many turnovers, too much reckless play," Bruins coach Bruce Cassidy said. "So we've got to do a better job coaching them up. No doubt. That's on us. By the same token, once they get on the ice, they have to recognize how they can help us win games. So that's the one thing we've got to correct."
It was the first time the Rangers played at home in front of fans this season. There were 1,800 people permitted per state regulations allowing no more than 10 percent capacity.
"We definitely got a bit of a spark, there's no doubt," Strome said. "Standing there during the national anthem I had some goose bumps and some energy that I haven't felt in a long time."
The teams are scheduled to play here again Sunday (Noon ET; NBC).
The Rangers scored two goals in 12 seconds late in the second period.
Colin Blackwell scored a power-play goal with a redirection of Fox's shot for a 3-1 lead at 18:52. The Rangers then lost the face-off, but Kreider won a puck battle on the forecheck and whipped in a shot from the bottom of the right circle to make it 4-1 at 19:08.
"You've seen earlier in the year our ability to hold those one-goal leads wasn't great, but to get those two late ones was obviously huge," Fox said. "You definitely feel a lot more comfortable coming out for the third with a three-goal lead as opposed to a one goal lead. It was definitely good for us, and we obviously came out strong and got some goals quickly [in the third]."