With the score tied 1-1 and the Oilers' Ryan Smyth in the penalty box, Sam Gagne burst into the Columbus zone and skated down the right side.
He threaded a backhanded pass to Paajarvi in the slot, and the Edmonton forward sent it over the shoulder of Sergei Bobrovsky for his first goal of the year.
Gagner later added an empty-netter and Ales Hemsky also scored as the Oilers logged their first win since Jan. 30.
Devan Dubnyk earned the victory, turning away a season-high 39-of-40 shots.
R.J. Umberger scored and Bobrovsky finished with 11 saves as the Blue Jackets dropped a third straight.