Vanek finished with a goal and two assists, while Nathan Gerbe scored twice, including a highlight reel spin-around goal that tied it midway through the third period. The Sabres had already secured a postseason spot by earning a point when the game entered overtime.
With the win, they've clinched at least seventh place in the Eastern Conference standings.
Danny Briere and Scott Hartnell had a goal and assist, and Kris Versteeg also scored for Philadelphia, which is winless in its past five games (0-3-2).