The Coyotes' losing streak knocked them out of first place in the Pacific Division. Phoenix trails Dallas by three points for the division lead, but moved within three points of Chicago for the No. 6 seed in the Western Conference.
San Jose, which has lost five straight, slipped a point behind Colorado in the race for the final playoff berth in the West.
The five shutouts are a single-season high for Smith in his six-year career.
Antti Niemi gave up the three goals on 29 shots.
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