Adin Hill made 23 saves after Antti Raanta was a late scratch with a lower-body injury for the Coyotes (12-13-4), who were outscored 11-1 in the three-game set.
"It's no secret, for whatever reason we're having a hard time getting just one (goal) past the opposing team right now," Arizona forward Christian Fischer said. "Who [cares] if we're scoring seven goals or one. We need to win games, and right now we're in the dump. But no one feels bad for themselves. We need to stop this right now, otherwise we're going to get ourselves in a hole. It's pretty simple, we need to work our way out."
Hartman gave Minnesota a 1-0 lead at 1:37 of the first period when he shot into an open net after Jordan Greenway's initial attempt ricocheted off the end boards to him in the right circle.
Coyotes forward Clayton Keller had a chance to tie it on a breakaway at 5:17 of the second period, but his wrist shot was stopped in tight by Kahkonen.
"We've had seven or eight breakaways in three games, we haven't scored," Arizona coach Rick Tocchet said. "You get one there, maybe loosen some guys up, you can just tell, and then things snowball.
"We're getting tested. People are testing us, adversity's testing us. Everybody in their career has to go through adversity, and this is one that's hitting our team right now."
Zuccarello made it 2-0 with a wrist shot from the top of the left circle at 2:07 of the third period, and Spurgeon scored his first of the season with a slap shot from just inside the blue line to extend the lead to 3-0 at 13:57.
"I think we'd been wanting to go out there every game and try to get the first goal, try to get the second goal, just get a lead," Kahkonen said. "It's obviously for those guys [it's] much more fun to play with the lead. To me, it's pretty much the same job: Just try to stop the puck. But obviously, it's nice, and it's nice that a lot of different guys are getting goals too."
