Elliott, who blanked Detroit by an identical 1-0 score Sunday, needed only 15 saves to extend the Blues' winning streak to five games.
Alexander Steel scored the only goal of the game on a slap shot at 16:37 of the second period in a game in which only one 2 minute penalty was called. The Blues took 26 shots on Nashville goaltender Pekka Rinne.
Nashville, which has been hobbled by injuries, lost its fourth consecutive game and fell to 1-5-2 since March 28.
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