Vanek, the top goal-scorer for Buffalo the last five seasons, set the tone with his first goal at 4:02 in the first period. Ville Leino of Finland, playing in his former home stadium, then made it 2-0 on his debut for the Sabres.
Nate Guenin replied for Anaheim in the second period, but Vanek helped restore the Sabres' two-goal lead by setting up Jason Pominville.
Vanek then scored his second of the night later in the period. Pominville also had two assists, as did Luke Adam.
"The puck was bouncing for us a bit tonight and we played a good first period with the two-goal lead," Vanek said. "We tried to get pucks to the net and it paid off early on."