The Bolts went on a 4-on-3 power play when Eric Brewer was whistled for holding and Lecavalier made St. Louis pay with a backhander past Ty Conklin for the game-winner in the waning seconds of the extra frame.
Steven Stamkos scored his NHL-best 40th goal and racked up three assists for the Southeast Division-leading Lightning, who extended their lead over Washington to three points with the victory.
Dan Ellis stopped 29-of-32 shots while Dominic Moore and Steve Downie also scored for the victors.
David Backes, Patrik Berglund and Nikita Nikitin found the net and Conklin ended with 36 saves for the Blues.
Celebrity Families of 2014 [PHOTOS]