Vancouver twice trailed by a goal, but the Canucks put together three straight scores to take command.
Jason Garrison and Sedin scored 1:46 apart in the third period with Sedin's goal coming 4:18 into the stanza.
Brenden Morrow brought the Stars within one with 13:53 still to play, but the Stars could not get another shot past Cory Schneider.
Schneider made 22 saves while backup goaltender Cristopher Nilstorp surrendered all four goals on 22 shots.
2014: The Year in Music [PHOTOS]