Smith's shutout was the 20th of his career and was his first victory over the season after missing five games with a pulled groin.
Mikkel Boedker and Nick Johnson scored for Phoenix, which was coming off a 4-3 overtime loss to the Stars Friday.
Richard Bachman turned aside 32-of-34 shots for Dallas, which fell for the fifth time in six games overall.
Aaron Carter is still in love with Hilary Duff
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