Elliot's whitewash was his ninth of the season, giving him the NHL lead over Jonathan Quick of Los Angeles and the New York Rangers' Henrik Lundqvist.
Elliott set a club record, going 186 minutes, 33 seconds, without allowing a goal.
Pekka Rinne took the loss, yielding three goals on 24 shots.
Nashville's lead over Chicago for the West's fifth seed decreased to three points with the loss.
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