Stamkos scored his league-leading 23rd goal of the season off a deflection past Ryan Miller at 16:01 of the first period.
St. Louis extended the lead to 2-0 at 8:15 of the second period with a power-play goal off a sharp pass from Teddy Purcell.
The Lightning ended a three-game losing streak while Buffalo failed to make up ground in the race for the final playoff spot in the Eastern Conference.
Jordan Leopold scored for Buffalo at 16:52 of the third period.
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