Faulk forged a 2-2 tie with 6 minutes remaining in regulation when his long shot from the point snuck past Boston goalie Tim Thomas.
Then with 2 1/2 minutes left, Harrison intercepted a clearing pass and got off a shot from the deep slot that went through a maze of traffic for the go-ahead tally.
Eric Stall quickly followed with an empty-netter as Carolina won its second straight game.
Patrick Dwyer also scored and Cam Ward made 33 saves in the victory.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut