Goals by Brad Marchand and Shawn Thornton each gave the Bruins an advantage in the final frame, but New Jersey's Nick Palmieri responded with two goals to keep the Devils in it.
Pouliot's goal off the rebound of a Joe Corvo shot with 3 minutes left, however, proved to be the game-winner as the Bruins notched their sixth straight victory.
Tim Thomas stopped 27 shots in the win.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys