Ales Kotalik and Erik Christensen each had a goal while Ryan Callahan and Brandon Dubinsky donated two assists each for the Rangers, who had dropped three of four coming into the game. Henrik Lundqvist stopped 26 shots in the win.
Boston had rallied from a 2-0 deficit with a pair of goals in 1:26 in the latter stages of the third period.
The Rangers, though, took a 3-2 lead as Higgins skated down the left side and before he went behind the net he snuck the puck past the right pad of Rask, who was starting to sneak over to the other side.
Boston pulled Rask shortly after the goal for an extra attacker, but was unable to net the equalizer.
The Rangers struck first on the power play midway through the first period as Dubinsky slid the puck over to the top of the left circle where Kotalik let fly with a one-timer past Rask.
At the 7:34 mark of the second period, New York took a 2-0 lead as Christensen skated into the Boston end down the right wing, cut to the front of the net and slid a backhander past Rask for his second goal of the season.
Boston finally got on the board with 5:27 to play to make it a 2-1 game. A slap shot by David Krejci hit Wheeler in front, but the puck went right to Hunwick and he backhanded it in for a shorthanded goal.
Just 1:26 later, the Bruins tied the game as Michael Ryder fed the puck from the left boards to the slot where Wheeler corralled it and wristed the puck over the glove of Lundqvist.
The Rangers host Dallas on Wednesday...Boston plays in Ottawa on Tuesday...The Rangers beat Boston, 1-0, in New York on November 1...New York went 1-for-5 on the power play while Boston failed to score on any of its three chances.