All eight goals in regulation came during the second period, in which Stamkos opened and closed the scoring.
Tampa Bay improved to 4-1 at home this season and snapped Chicago's three-game winning streak.
Lecavalier had one assist during the wild second period and scored the game-winner on a wrist shot for his sixth goal of the year.
Stamkos opened the scoring 15 seconds into the middle period, but midway through the stanza Chicago owned a 4-2 advantage. Stamkos then scored with 8:15 to go and finished off the eight-goal period by putting a slap shot past Ray Emery on the power play with 33 seconds left.
Patrick Sharp had two goals for the Blackhawks to give him five for the campaign.
Dwayne Roloson made 28 saves to get the win. Emery stopped 26-of-31 shots.
Celebrity Families of 2014 [PHOTOS]