Smith improved to 7-2-3 on the season with the 31-save performance, in which he weathered 13 third-period shots as San Jose fought to get back into the game.
Radim Vrbata and Boyd Gordon staked Smith to a 2-0 lead with first-period goals, and Patrick O'Sullivan added a marker in the third as the Coyotes won for only the second time in 12 meetings with the Sharks.
Thomas Greiss stopped 20-of-23 shots for San Jose.
Ray Liotta sues skin care company over use of likeness
Boston schools pull out free condoms over wrapping complaints