After neither of the teams managed to score in the first period, they put on an offensive show over the final 40 minutes. The Sabres snapped a four-game losing streak and handed the Bruins their first loss in regulation this season.
Both sides scored three times in the second period with Vanek producing two of the goals and Brad Marchand recording two for the Bruins.
Boston then took a 4-3 lead 1:45 into the final period on a backhander from David Krejci, but Buffalo produced the game's final four scores.
Alexander Sulzer tied it with 2:28 having elapsed in the third and Cody Hodgson put the Sabres in front 4 minutes later.
Vanek completed his hat trick with 1:31 to play and Jason Pominville added an empty-net goal with 14 seconds remaining. Vanek's three goals equaled his total output in his first five outings of the campaign and he added two assists.
He sat out last Tuesday's overtime loss to Toronto with an undisclosed injury.