With new head coach Jon Cooper watching from an executive suite, the Lightning put together one of their most complete defensive efforts this season.
Cooper is set to coach his first game on Friday against the New Jersey Devils.
Buffalo, which came into the game riding a three-game winning streak, was held to just 14 shots.
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.
Ryan Miller had 21 saves for the Sabres.
Lightning general manager Steve Yzerman released a statement on the death of former assistant coach Wayne Fleming: "It is with a heavy heart that we acknowledge the passing of Wayne Fleming. Wayne was an extremely important part of the Lightning family on and off the ice during his time here. The thoughts and prayers of the entire Lightning organization go out to Wayne's wife, Carolyn, and the entire Fleming family."