The Sabres also got a goal from Derek Roy. Buffalo has won consecutive games after a four-game losing streak to extend its lead over New Jersey for the conference's best record to four points.
Tampa Bay's Vincent Lecavalier scored twice, giving him an NHL-leading 48 goals. He set a team record with 96 points this season.
The Lightning played at home for the first time since going 3-3 on a road trip. Tampa Bay trails Southeast Division-leading Atlanta by four points.
Lecavalier put the Lightning up 1-0 early in the first before Buffalo responded with three goals midway through the period.
Pominville tied it at one at 7:29 from a tough angle near the goal line. After Roy was credited with a goal following a video review at 8:05, Pominville made it 3-1 with 9:36 left.
Lecavalier pulled the Lightning to 3-2 with 15:22 remaining in the third.
Miller stopped Brad Richards' in-close shot with 1:35 to play.
Notes: Tampa Bay RW Martin St. Louis held the previous team points record with 94, set during the 2003-04 season. ... Buffalo C Daniel Briere had two assists, extending his points streak to four games. He has five assists and seven points during the stretch. ... Lecavalier has seven goals and 12 points during a seven-game points streak.