Marian Hossa, Ryan Hartman and Patrick Kane all scored in the first and the Blackhawks held on for a 4-3 win over the Coyotes. Artemi Panarin lit the lamp in the second to help Chicago end a three-game slide.
Oliver Ekman-Larsson, Christian Dvorak and Brendan Perlini all found the back of the net in the second for Arizona, which has lost its last two.
The Blackhawks will be in Dallas on Saturday.