Rask stopped 10 shots in each of the first two periods as the Bruins were posting a 2-0 lead on tallies from Jaromir Jagr and Dougie Hamilton.
The Finnish goaltender's shutout was his fourth of the season and helped Boston snap a four-game losing streak.
Brad Marchand added an empty-netter to punctuate the victory, which gave the Bruins 59 points and earned them a tie them with the idle Montreal Canadiens atop the Northwest Division standings.
Boston holds a games in hand over the Canadiens with four contests remaining.
Jacob Markstrom made 36 saves in the Panthers' loss.
Celebrity Families of 2014 [PHOTOS]