Pouliot's tally with 9 1/2 minutes left in the game broke a 2-2 tie and opened the floodgates for the Bruins, who followed with goals from Brad Marchand and Rich Peverley to put the contest away.
Tim Thomas made 16 stops for the Bruins.
Steven Stamkos scored twice for the Lightning, giving him an NHL-best 55 goals for the season.
Tampa Bay's Dwayne Roloson yielded four goals on 37 shots.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys