Halak stopped all 19 Panthers shots to surpass Hall-of-Famer Glenn Hall for the all-time St. Louis shutout mark. Hall registered 16 whitewashes for the Blues from 1968-71.
Brenden Morrow ignited a five-goal, second-period outburst with a power-play goal. Vladimir Tarasenko, Jaden Schwartz, Derek Roy and Alex Steen also each scored for St. Louis before the middle period was over.
Ryan Reaves and Patrik Berglund scored in the third for the Blues.
Florida's Tim Thomas, making his first NHL start in a year, was chased in the second after yielding five goals on 28 shots.
Jacob Markstrom played the rest of the way, giving up two goals on six shots.