Hossa scored Chicago's first goal when his team had a two-man advantage in the first period.
Hossa skated Tuesday for the first time since Thursday. He missed Saturday's game against the Boston Bruins with an undisclosed upper body injury.
"I'll know more in a few hours," Hossa said. "I'm actually surprised because (Monday) I felt a little worse."
The Hawks took on the Coyotes for the first time this season and they faced former Vancouver Canucks winger Raffi Torres for the first time since Torres knocked out Hawks defenseman Brent Seabrook with a head shot during last year's playoffs. Torres was given just a minor penalty on the play.
"He plays very physical, he plays with an edge and sometimes he might cross the line," Jonathan Toews said. "So you have to watch out for him but if you get the chance to get a lick on him, you might as well go ahead and take it."
Corey Crawford started in goal for the Hawks.
Jesse Rogers covers the Blackhawks for ESPN 1000 and ESPNChicago.com.