"It was a good effort," Coyotes coach Rick Tocchet said. "We're getting some chances. I don't think we're getting enough net-front [presence]. That's something over the summer we've got to start to find. We need people who can go to the net."
Niederreiter gave Minnesota a 1-0 lead at 7:35 of the first period with a power-play goal. Raanta saved Matt Dumba's one-timer from the top of the left face-off circle, but Niederreiter gathered the rebound and scored from the top of the crease.
Keller scored on a breakaway at 4:03 of the second period to tie it 1-1. Richard Panik blocked Wild defenseman Ryan Murphy's shot at the blue line, and passed to Keller who beat Dubnyk five-hole with a backhand.
The goal was Keller's 20th of the season, which is two shy of the Coyotes rookie record set by Peter Mueller in 2007-08, and his 52 points are two points shy of the rookie record also held by Mueller.
Panik had a chance to give Arizona the lead on a breakaway at 13:59 of the second period, but Dubnyk made a glove save.
"It was a short time spent here, but this organization gave me my confidence back and believed in me and gave me a chance," said Dubnyk, who played 19 games with Arizona in the 2014-15 season. "They'll always kind of hold a special place for me."
Foligno scored at 10:51 of the third period to make it 2-1. After Joel Eriksson Ek forced a turnover behind the net by Coyotes defenseman Jakob Chychrun, Daniel Winnik collected the puck and passed to Foligno, who scored from the right circle.
Staal scored an empty-net goal with 17.9 seconds left to extend it to 3-1.