Jason Pominville had two goals and two assists and the Sabres scored six times on their final 10 shots to overcome a 4-1 deficit. Derek Roy had a goal and two assists and Drew Stafford set up three goals in helping Buffalo inch within a point of Philadelphia for the Eastern Conference's eighth and final playoff berth.
The Sabres overcame a three-goal deficit for the first time since a 5-4 victory against Toronto on March 23, 2007. And it marked their third come-from-behind victory against the Lightning this season. Buffalo rallied from a pair of two-goal deficits, including a 4-3 overtime victory on Feb. 20.
The Sabres swept the four-game series against Tampa Bay, with Vanek producing three game winners.
Vincent Lecavalier scored twice, including his 39th of the season, for the Lightning, the East's last-place team, which had a three-game winning streak snapped.
Down 4-1, the Sabres scored four times in an eight-minute span, with Vanek putting the Sabres ahead for good with 6:46 remaining. Roy set up the play by beating defender Shane O'Brien to the puck in the right corner, and feeding Vanek in the high slot.
Vanek sidestepped Junior Lessard, and snapped a low shot that sneaked inside the right post past screened goalie Karri Ramo.