Raffi Torres added his 12th goal of the season early in the third period for Phoenix, which ended a five-game losing streak. The Coyotes have 78 points and are in seventh place in the Western Conference.
Smith earned his 16th career shutout, and the fifth this season. Smith's previous shutout was Feb. 16 against the Kings.
Antti Niemi made 26 saves for San Jose, which has lost five straight and seven of its past eight games. The Sharks have 75 points and trail eighth-place Colorado by one point in the West.