After Pavel Kubina handed the Lightning a 1-0 lead with slap shot in the second period.
Tampa Bay doubled the advantage 8:30 into the final frame when Vincent Lecavlier picked up a turnover at his own blue line and found St. Louis all alone in front of Sabres goalie Ryan Miller.
The Lightning forward deked Miller to the ice and fired it into the upper left corner for the score.
St. Louis also assisted on Victor Hedman's goal for the Bolts, who beat Buffalo for the 11th time in 13 home meetings.
Garon turned aside all 21 shots he saw for Tampa Bay.
Miller finished with 23 saves as Buffalo fell short in its bid to sweep a four-game road trip.