Dany Heatley scored just 13 seconds into the contest to put the Wild in front, but they could not score again until just 4:02 remained in the contest.
Sedin's power-play tally tied it with 5:56 to go in the opening period and Maxim Lapierre put Vancouver in front for good with 42 seconds to go in the stanza.
Vancouver has earned at least one point in each of its last eight games (6-0-2). The Canucks' previous five contests had all gone into overtime.
Henrik Sedin played in his 553rd consecutive game despite suffering a deep ankle bruise on Tuesday when he blocked a puck against Nashville.
Cory Schneider made 22 saves for the Canucks. Niklas Backstrom allowed four goals on 19 shots.
Notable deaths of 2014 [PHOTOS]