Vesey tied it 1-1 at 10:21 of the second, scoring on a redirection of Mika Zibanejad's pass from the right circle into the slot.
Boston forward A.J. Greer was given a two-minute instigator minor 36 seconds later for going after Schneider after he laid a hard hit on Frederic.
The result was a power play for the Rangers, but the Bruins said they were happy to kill it off because of how Greer stood up for Frederic.
"That gave our bench a lot of momentum," Montgomery said.
Coyle scored the first goal of the third, giving Boston a 2-1 lead at 2:56 with a tap-in from in front of the left post after Lindholm slid him a wraparound pass through the crease.
Coyle, who has a goal in four straight games, used his stick to gain position and make himself available for the tap-in.
"I don't even know if I had that great of position, but he just put it on a tee for me," Coyle said.
Fox scored 48 seconds later with a wrist shot from above the right circle to make it 2-2.
But the Bruins quickly regained the lead 3-2 with Frederic scoring at 6:04. DeBrusk then scored on a one-timer from Taylor Hall at 10:19 to make it 4-2.
Lindholm scored an empty-net goal from nearly the length of the ice at 19:02 for the 5-2 final.
"This was the best game management game we've had without the puck," Montgomery said. "The Rangers are a really good hockey team and they had us on the ropes there [in the second], but we kept them to the outside. That's really good team defense."
NOTES: Ullmark improved to 8-0-0, tying a Bruins record for the most consecutive wins by a goalie to start a season (Tim Thomas, 2010-11). … The Bruins announced defenseman Derek Forbort underwent surgery on his right middle finger and will miss 4-6 weeks. Forbort was injured in a 6-5 overtime win at the Pittsburgh Penguins on Tuesday. … Zibanejad had an assist on Vesey's goal to extend his point streak to four games (two goals, four assists).