Jordan Greenway also scored, and Devan Dubnyk made 19 saves for Minnesota (24-21-3).
Forward Victor Rask had an assist in his debut with the Wild after being acquired in a trade that sent forward Nino Niederreiter to the Carolina Hurricanes on Thursday. Rask centered the line between Parise and Pontus Aberg, who was acquired from the Anaheim Ducks on Wednesday for forward Justin Kloos. Aberg had the primary assist on Parise's goal.
WATCH: [All Blue Jackets vs. Wild highlights]
"I think we're going to learn more about each other as we go," Parise said. "[They're] skilled guys, good on the offensive side. I feel like we could've had a couple more. Victor hit the post on a breakaway, I just missed Pontus on the back side there. But it was a good Game 1 for us, I thought."
Artemi Panarin scored, and Sergei Bobrovsky made 29 saves for Columbus (28-17-3) which lost its second game in a row.
"We were a sloppy bunch, but we still have a chance," Blue Jackets coach John Tortorella said. "[Bobrovsky] gives us a chance. We wasted a great effort by [Bobrovsky]. It's mind-boggling what we do when we get near that net and how many pucks we shoot wide or overhandle."
Greenway gave the Wild a 1-0 lead when he one-timed a backhand pass from Eric Staal at 16:07 of the first period.
Parise's 20th goal made it 2-0 when he scored from the slot at 17:36 of the first. He has 13 points (five goals, eight assists) in his past 13 games.
Panarin scored a power-play goal at 3:07 of the second period to make it 2-1. It was his 19th of the season.
"Any time we win, I'm happy," Wild coach Bruce Boudreau said. "There's so many teams that are hitting their sense of urgency right now, which is right now a lot earlier than normal. … I've got to believe it's going to be quite a race from here on in."
