Vanek scored two goals in each of the first and second periods as the Sabres beat the Senators for the first time since January 6, 2009. The goals boosted Vanek's season's total to 27.
Derek Roy had the Northeast Division winners' fifth goal in the third. He also assisted on two of Vanek's scores.
Chris Neil brought Ottawa within 2-1 in the second before Vanek scored his third and fourth goals.
The Senators' Shean Donovan completed the scoring with more than six minutes to play in the third.
Ottawa, however, will be without key forward Alex Kovalev during the play-offs after it was confirmed he would require surgery on a torn anterior cruciate ligament in his left knee.
Kovalev, acquired last summer, suffered the injury in Thursday's loss to the Tampa Bay Lightning.
Senators' general manager Bryan Murray said on Saturday the normal rehabilitation period was up to four months.
(Reporting by Gene Cherry in Salvo, North Carolina; Editing by Greg Stutchbury)