Jaden Schwartz scored in regulation for the Blues, who are 15-3 in their last 18 games. Brian Elliott stopped 40 shots, including 20 in the third period and two in overtime.
The Blues earned their third consecutive win and sixth in a row over the Panthers. Florida hasn't defeated St. Louis since a 4-0 victory on Oct. 31, 2009.
Nick Bjugstad scored for the Panthers, and Luongo made 32 saves.
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