GLENDALE, Ariz. -- Peter Mueller had little trouble expressing his relief after scoring his first goal of the season.
Mueller spent two games as a healthy scratch before returning to the lineup Wednesday in Colorado. Though he didn't record a point, extending his scoreless streak to seven games, Phoenix coach Dave Tippett saw an immediate difference.
"He sat out a couple of games and it hopefully helped him get his urgency back," Tippett said. "There's an urgency in the details in what he's doing in practice. He's not so nonchalant, and that has shown the last two games."
Scottie Upshall also scored, and Ilya Bryzgalov made 31 saves for the Coyotes, who snapped a two-game losing streak.
"Everyone was in together," Bryzgalov said. "There were no passengers tonight. Everybody did his role."
Kris Versteeg had a short-handed goal for the Blackhawks, who have lost two of three.
"They're a better team," Chicago coach Joel Quenneville said of the Coyotes. "They're deeper, they're balanced, they have a very mobile defense and they've got good goaltending."
Hanzal needed just 2:34 to give the Coyotes a 1-0 lead, sending a sharp wrist shot from the middle of the left circle between Cristobal Huet's pads.
Mueller made it 2-0 at 11:55 on a rebound after Hanzal tried to redirect a pass from Shane Doan from the half-boards.
Upshall extended the lead to 3-0 at 10:38 of the second period with a wrist shot from the left circle just inside the right post.
Versteeg brought the Blackhawks within 3-1 at 13:56 of the second period, taking a back pass from Patrick Kane and beating Bryzgalov with a wrister from the left circle. Despite being short-handed, Chicago spent most of the first 90 seconds of the power play cycling in the Coyotes' zone before scoring.
Colin Fraser appeared to cut the deficit to one with 9:20 remaining, but the apparent goal was overturned by video review which showed that Fraser kicked in the puck.
"We've got to bear down and try to get to those opportunities," Versteeg said. "If we score on half our opportunities it's totally a different game."
Coyotes D Ed Jovanovski left late in the third period with an apparent lower-body injury. The announced crowd of 10,362 was the third-highest of the season. Kane and Patrick Sharp missed on consecutive breakaway attempts early in the second period. Blackhawks C Jonathan Toews (concussion) skated before the game, but missed his fifth straight contest. Toews was injured on Oct. 21 and might return to the lineup on Friday. Phoenix was without Zbynek Michalek, who sustained a lower-body injury in the Coyotes' 4-1 loss to Colorado on Wednesday and is listed as "week to week." Kane has six points in six games.