Backstrom turned back all 12 of the Canucks shots he faced in the third period as the Wild got goals from Charlie Coyle and Matt Cullen to break open a 1-1 contest.
Jonas Brodin also scored for Minnesota, which ended an 11-game winless streak in Vancouver and increased its lead over the second-place Canucks to two points in the Northwest Division.
Henrik Sedin notched the only goal for Vancouver, which fell for the fourth time in six games.
Roberto Luongo made 22 saves in the loss.
2014: The Year in Music [PHOTOS]