Backstrom, starting his second straight game in place of Manny Fernandez, signed as a free agent on June 1. He posted 18 shutouts the past four seasons while playing the Finnish Elite League. Pierre-Marc Bouchard and Branko Radivojevic scored power-play goals, Pascal Dupuis added a short-handed tally, and Mark Parrish scored at even strength for the Wild, 9-1-1 at home. Kurtis Foster and Todd White each had two assists.
Curtis Joseph was shaky in stopping 18 shots for Phoenix and was replaced by David Leneveu after Radivojevic made it 4-0 at 6:57 of the third period.
The Coyotes, who lost for the third time in four games, are an NHL-worst 1-9 on the road.
Phoenix, which has the league's 29th-ranked power play, was 0-for-5 with the extra man. Minnesota, which has the league's best home power play and fourth overall, was 2-for-6.
The Wild took a 1-0 lead late in the first period during one of their two 5-on-3 advantages.
Foster raced to a loose puck at the point and poked it ahead to White, who used a touch pass to find Bouchard alone in front. Bouchard moved the puck from backhand to forehand, before deking Joseph, who lost for the second time in 12 career starts against Minnesota.
After Parrish beat Joseph with a slapshot between the pads midway through the second period, Brian Rolston avoided a slash by Ladislav Nagy, to begin a 2-on-1 late in the period. Dupuis took a pass from Rolston in the right circle, and held the puck for a few seconds before putting a wrist shot between Joseph's pads for his fourth goal in five games.
Radivojevic scored his first goal in 10 games by putting a rebound of Foster's shot into an open net midway through the third.
Notes: Bouchard's goal was his first point in six games. ... Phoenix is 2-12 when its opponent scores first and 1-15 when trailing after two periods. ... Minnesota C Pavol Demitra missed his second straight game with a head injury, and C Wes Walz sat out his second game due to a hip injury.