Phoenix moved into the lead in the Pacific Division, one point in front of Dallas. The Stars suffered a 2-1 loss to Vancouver earlier in the evening.
Daymond Langkow and Kyle Chipchura scored for the Coyotes in the first period and Torres gave Phoenix a seemingly comfortable advantage with 3:05 to go in the second.
Smith held on, however, to pick up the 100th win of his NHL career. He finished with 39 saves.
The three Phoenix goals were scored against Semyon Varlamov on 25 shots.