Canucks goalie Richard Bachman (23 saves) made an errant pass from behind his net that went directly to Koivu, who shot into the open net to make it 2-0 at 7:43 with a power-play goal.
"It happens sometimes, and mistakes are a part of the game," Koivu said. "I'm sure he'd like to get that one back."
Bachman said: "I just fanned on it. Most times, I'll get those up, out and down the ice. It [stinks] it didn't happen. I was a little, maybe I was overthinking just a little because it had been awhile. Bad bounce, bad play by me, bad execution. If I'm going to do that, I've got to get it out. But things happen in hockey. Next time, better go off the glass with it."
Nino Niederreiter redirected a no-look pass from Koivu in the slot for a power-play goal 1:56 into the second period to give the Wild a 3-0 lead.
Horvat made it 3-1 with a power-play goal at 6:26, but Eric Staal scored 36 seconds later on a wraparound to make it 4-1 at 7:02.
"I thought we came out with some energy," Horvat said. "We knew it was going to be the last game of the road trip and knew they were going to come hard. I think they got a couple right away, and I think that kind of took the wind out of our sails a little bit and we just didn't do the right things to get the job done tonight."
JT Brown backhanded a pass to defenseman Matt Dumba at the point for a one-timer that increased Minnesota's lead to 5-1 at 13:12.
Jason Zucker one-timed a backdoor pass from Staal at 5:27 of the third period to make it 6-1.
Granlund scored 27 seconds later to make it 6-2 at 5:53.
The Wild were without forward Zach Parise, who missed the game with an illness.
"They lose a guy like Parise and their top six looks pretty good still," Canucks coach Travis Green said. "That's a good team."