Smith was busiest in the second period, making 12 saves as Phoenix handed the Penguins their first regulation loss in 10 games against Pacific Division foes this season.
Radim Vrbata also scored as the Coyotes won for the third time in seven games.
Evgeni Malkin scored the only goal for Pittsburgh, which went 1-1-0 on a two-game Western Conference trip.
Marc-Andre Fleury made 27 saves.
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