Hartman put Minnesota back in front 2-1 on the power play at 18:16, one-timing a backdoor pass from Kaprizov at the right post.
"It's always good to score,” Hartman said. “Obviously, you're trying to help the team win, and in that aspect you need scoring from around the lineup. It helps this team a lot, and I'm trying to continue to do that."
Vejmelka made a pad save on a Mats Zuccarello breakaway at 11:04 of the third period to keep it a one-goal game.
Kaprizov pushed it to 3-1 at 17:28 with an empty-net goal, and Foligno also scored into an empty net 27 seconds later at 17:55 for the 4-1 final.
“I think we got outworked all night, to be honest,” Coyotes forward Michael Carcone said. “We weren't breaking pucks out, weren't putting pucks behind them. They played a good game and kind of took it to us tonight."
NOTES: Coyotes forward Barrett Hayton was a late scratch with a lower-body injury. Tourigny said Hayton is back in Phoenix to be examined further and that “it's not a day-to-day injury. It will be longer than that." … Wild forward Joel Eriksson Ek left the game at 2:55 of the third period following a hit from Bjugstad. There was no update. … Kaprizov had his 25th multigoal game in the NHL, tied with Zach Parise for the second-most in Wild history behind Marian Gaborik (41).