Buffalo's first two shooters, Vanek and Nathan Gerbe, also were stopped before Stafford beat Anton Khudobin.
And Gerbe, who played at Boston College, acknowledged he's "a little nervous" about traveling to Boston.
"You're worried because they don't know exactly why and how and who, " Gerbe said.
Gerbe has four goals this season and three of them have come against the Panthers.
Tomas Kaberle sat out for Montreal, while Nathan Gerbe and John Scott were Buffalo's scratches.
Gerbe then broke up a pass and his shot beat Henrik Lundqvist high on the glove side.
Marcus Foligno, Drew Stafford, Andrej Sekera, and Nathan Gerbe scored for the Sabres and Ryan Miller stopped 36 shots.
Buffalo forward Nathan Gerbe tried to rough up Giroux along the back boards with hits to the back and head.
Gerbe scored on the Sabres' second shootout attempt by snapping a shot that beat Martin Brodeur low on the glove side.
Luke Schenn stood up for Giroux and sent Gerbe into the boards.
Cody Hodgson, Nathan Gerbe, Drew Stafford and Mark Pysyk scored for Buffalo, which was eliminated from the postseason picture and had its three-game winning streak stopped.
Just 32 seconds after Gerbe's goal, Callahan stole the puck from Buffalo's Mike Weber and his forehand beat Enroth on the glove side for a 7-2 lead.
"Life's way more important than hockey, " forward Nathan Gerbe said.
The Sabres made it 2-1 less than a minute later when Gerbe took a shot from above the right circle near the boards that deflected off a Panthers player and into the net at 1:36.
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