Smith, who allowed only 12 goals over the six-game Western Conference quarterfinal series, was especially busy in the first period Monday when he turned aside 16 Blackhawks shots.
Gilbert Brule, Kyle Chipchura and Oliver Ekman-Larsson each contributed a goal and an assist for the third-seeded Coyotes, who eliminated Chicago 4-games-to-2 to win their first playoff series since the franchise was known as the Winnipeg Jets.
Antoine Vermette also scored for Phoenix.
Corey Crawford turned aside 20 shots for Chicago, which lost in the first round for the second straight year following its 2010 Stanley Cup championship.
Celebrity Families of 2014 [PHOTOS]