Stamkos became the first NHL player to reach the 20-goal mark with what turned out to be the game-winner midway through the final frame off a feed from Vincent Lecavalier.
Blair Jones and Eric Brewer also scored for the Lightning, who won for just the third time in 10 games.
Garon, a former Blue Jacket who left the team to sign a two-deal deal with the Lightning during the off-season, stopped all 12 shots he saw in the final period.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys