Carter's power-play goal 4:42 into the game gave Philadelphia a lead it wouldn't relinquish and the second-seeded Flyers seized the advantage in their Eastern Conference quarterfinal series with a road win over the Sabres.
Brian Boucher turned aside 35-of-37 shots, including all 11 he faced in the third period, while blanking Buffalo on 4-of-5 of power-play opportunities.
Danny Briere and Nikolay Zherdev scored and Kimmo Timonen added an empty-netter in the Flyers' victory.
Drew Stafford and Nathan Gerbe scored and Ryan Miller made 22 stops for the seventh-seeded Sabres.
Buffalo will host Game 4 of the series Wednesday.
Notable deaths of 2014 [PHOTOS]