The Coyotes overcame a two-goal deficit in the third period but could not ride that momentum to a win.
Vancouver captured its third in a row with Roberto Luongo making 36 saves in the victory.
Jason Garrison and Henrik Sedin both scored in the second period to give the Canucks the lead. Sedin's goal came with just 57 seconds left in the middle stanza.
Mike Smith stopped 29 shots for the Coyotes.
Celebrity Families of 2014 [PHOTOS]