After Charlie Coyle one-timed a pass from Mikael Granlund to make it 2-0 during a power play in the third period, Pominville, acquired by Minnesota from Buffalo at last week's trade deadline, notched his first Wild goal with 1:25 left.
Pominville also assisted on Ryan Suter's second-period tally to open the scoring.
Backstrom made 24 stops in racking up his second shutout of the year for Minnesota, which rose to the sixth playoff seed in the Western Conference while breaking a three-game skid.
Sergei Bobrovsky stopped 21-of-24 shots for the Blue Jackets, who remained four points out of the East's post-season picture.
2014: The Year in Music [PHOTOS]