Rask stopped all 10 he shots he faced in the third period, which began with the Bruins clinging to a 2-1 lead.
Johnny Boychuk, however, gave Boston some insurance with 9:31 remaining, firing in a shot from the right boards after Carolina goalie Cam Ward was jostled by a collision in front of the net.
Carl Soderberg and Reilly Smith each supplied a goal with an assist and Milan Lucic added an empty-netter to keep the Bruins hot.
Ward yielded three goals on 29 shots in his first game since sustaining an Oct. 24 lower body injury.
Tuomo Ruutu got the Hurricanes' only goal.
2014: The Year in Music [PHOTOS]