Niklas Hjalmarsson and Andrew Shaw also each scored for the NHL-best Blackhawks, who dropped the first game of their sojourn but then reeled off six straight wins.
Antti Raanta, given the start in place of Corey Crawford, made 31 saves for Chicago.
Martin Hanzal and Rob Klinkhammer each scored for the Coyotes, who were handed just a second regulation loss in 13 home games.
Mike Smith stopped 31 shots.
2014: NFL Cheerleaders [PHOTOS]
Arizona Cardinals player formally charged