Antti Raanta made 17 saves in his return for the Coyotes (19-20-5) after missing 11 games with a lower-body injury.
"It's always different," he said. "You never know how you're going to feel when you come back from a little time off, but after those couple first bouncing pucks, you start to feel better. Overall, it was nice to get back playing, but the only thing that matters right now is to win and we didn't get it, so it's disappointment not for sure."
Jakob Chychrun and Phil Kessel scored for Arizona, which has lost five straight games in regulation and been outscored 21-11 in those games.
"We've got to win a game," Coyotes coach Rick Tocchet said. "We need to win a game just to get us feeling good about ourselves and just go from there. You can't win five in a row, you've got to win one at a time and that's what we have to do."
The Wild are third in the Honda West Division, 10 points ahead of the Coyotes, who are fifth. Arizona is one point behind the fourth-place St. Louis Blues. The top four teams will qualify for the Stanley Cup Playoffs.
"I think in the shortened season, we knew it'd be a sprint, but now it gets that much more tight," Bonino said. "Every play matters, I think guys are probably watching the standings a bit more than they were a month ago or two months ago. … What do we have, five left against [St. Louis]? That can directly impact where we fall in the standings. They're obviously of big importance here, the guys know that, and I think tonight was a good first step."