Stamkos, the NHL's leading goal-scorer, became the first player to reach 50 this season as the Lightning found the net three times within the game's first 4 1/2 minutes.
Ryan Shannon, Nate Thompson and Tom Pyatt got the early tallies and Tampa Bay went on to snap a three-game skid.
Dustin Tokarski turned aside 33-of-34 shots to collect his first NHL victory.
Turco stopped 8-of-12 shots for the game.
Jordan Caron netted the lone tally as Boston dropped its third straight and fifth in seven contests.
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