St. Louis recorded one goal and two assists and Brown added a pair of goals for the Lightning, who notched a fifth straight victory.
Valtteri Flippula chipped in a goal and assist and Victor Hedman supplied three assists for the streaking Bolts.
Alex Killorn and Tyler Johnson also scored and Ben Bishop earned the decision with 28 saves.
Sean Bergenheim got Florida's only goal.
Scott Clemmensen managed 30 saves on 36 shots.