Maxim Afinogenov also scored in helping the Sabres successfully open a season-high six-game homestand and end a four-game losing streak against their Northeast Division rivals. Backup goalie Martin Biron was sharp in making 28 saves.
Peter Schaefer and Dean McCammond scored for Ottawa, which dropped to 8-3-1 in its past 12.
The Sabres, who twice squandered one-goal leads, won despite playing on consecutive nights after a 4-3 shootout win at Atlanta. And they defeated a well-rested opponent - the Senators had been off since a 3-2 shootout loss against Toronto on Saturday.
Vanek's second goal came on the power play and during a wild scramble in front. Vanek's first shot from the slot - and with goalie Ray Emery out of position - was stopped by diving defenceman Anton Volchenkov. The puck caromed to the left circle, where Ales Kotalik fanned on his attempt, but the shot slid to the right post and Vanek slipped it into the open side.
The goal made up for a questionable penalty call that went against the Sabres earlier in the period, and led to Schaefer's goal, which tied the score at two.
Schaefer scored during a scramble, when he converted Mike Fisher's rebound.
The goal came on a Senators power play, when officials incorrectly penalized Teppo Numminen for delay of game after the Buffalo defenceman's clearing attempt went over the glass. Replays showed Numminen's backhander first hit the boards - which should have negated the penalty - before going out of play.
Questionable call aside, this marked the fifth time in seven games the Sabres have allowed an opponent to tie the score in the third period - with Buffalo losing three of those outings.
The game was a defensive stalemate between two of the Eastern Conference's most potent offences before Vanek and McAmmond traded goals 41 seconds apart just past the midpoint of the second period.
Vanek picked off Volchenkov's lazy cross-ice pass and drove untouched to the net to open the scoring. McAmmond tied it by poking in a rebound after Biron had difficulty controlling Joseph Corvo's shot from the right circle.
Notes: Retired defenceman Phil Housley was inducted into the Sabres' Hall of Fame in a pre-game ceremony. Drafted sixth overall by Buffalo in 1982, Housley played eight seasons with the Sabres and still ranks as the team's most productive defenceman with 558 points. The native of St. Paul, Minn., retired in 2003 with 1,232 points (338 goals, 894 assists), most among American-born players. ... Sabres D Jaroslav Spacek missed his third straight game with a knee injury. ... Ottawa penalty-killers went 3-for-4 and allowed only their seventh power-play goal in their past 20 games, a stretch in which they've killed off 75 of 82 attempts.