Vanek opened the scoring in the second and added two goals in the third, including his 20th of the season on a five-on-three with 3:58 remaining for his first three-goal game.
Clark MacArthur and Jason Pominville each had a goal and an assist in the third for the Sabres, who climbed back into the Eastern Conference playoff race by earning 16 of a possible 18 points while going undefeated through regulation in nine straight games.
Ryan Miller made 25 saves for Buffalo, which is 7-0-2 since Jan. 21, when a 6-2 loss in Phoenix dropped them to the conference's lower ranks with a 20-21-6 record.
Vanek scored the only goal of the first two periods 3:44 into the second with a slap shot past Ray Emery. He made it 2-0 early in the third as he spun around in front of Emery to beat the Ottawa goalie for his 19th goal.
Newcomer Cory Stillman got his first point with the Senators on an assist as Randy Robitaille ruined Miller's shutout bid with a power-play goal 3:57 into the third.
Senators public address announcer Stu Schwartz was still announcing details of Robitaille's goal when MacArthur restored Buffalo's two-goal lead 33 seconds later with his seventh goal at 4:30.