Smith notched 41 saves and carried the Coyotes, who were outshot 42-33 and weathered 17 shots in the third period.
Sean Doan blasted a power-play goal on a slap shot in the final seconds of the second period and Derek Morris and Kyle Chipchura chipped in goals as well for the Coyotes.
Jarret Stoll spoiled Smith's shutout bid at 16:39 of the third period on a power play. Ben Scrivens stopped 30-of-33 shots in goal.
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