Philadelphia maintained third place in the Metropolitan Division, two points ahead of Columbus, and won for the second time in eight games (2-4-2). With four games remaining, the Flyers trail the second-place New York Rangers by two points, but have a game in hand.
Schenn, Vincent Lecavalier and Zac Rinaldo scored second-period goals to put Philadelphia ahead 4-0. Matt Read also scored and Mark Streit had three assists.
Cory Hodgson and Mike Weber scored third-period goals for Buffalo, which lost its sixth straight road game and fell to 2-13-1 in its last 16 overall. The Sabres, assured of finishing with the fewest points in the NHL, have scored eight goals during their road skid.
Rinaldo was ejected in the third period, incurring a match penalty for a hit to the head of Chad Ruhwedel. Rinaldo, who entered with a team-high 137 penalty minutes, racked up 23 on Sunday and could face an NHL suspension.
Read got Philadelphia on the board 6½ minutes into the game by scoring on a rebound. After Buffalo's Cory Conacher turned the puck over, Streit fired a slap shot that caromed off the post to the slot, where a wide-open Read unleashed a wrister past rookie goalie Nathan Lieuwen.
The Flyers turned the game into a rout with three second-period goals. Rinaldo, known more for pesky play than scoring, scored his second of the season when his wrist shot went off Lieuwen's glove and trickled over the goal line to make it 2-0 with 12:20 left.
Schenn deflected in Streit's slap shot on the power play with 5:40 remaining, snapping the Flyers' 0-for-12 skid on the man-advantage and stretching the lead to three goals.
Lecavalier then put a shot over Lieuwen's right shoulder just over 1½ minutes later from the top of the right circle. Mason earned an assist on the goal for his first point of the season and seventh of his eight-year career.
Schenn scored his second goal with 4:50 left in the game when he fired a wrist shot past Lieuwen's glove.
Lieuwen, making his fifth career start, had 32 saves.
NOTES: The Sabres were without 10 injured players, including wingers Drew Stafford (33 points) and Chris Stewart (26), who entered ranked third and fifth in team scoring. Also out were Buffalo's top two goalies, Jhonas Enroth and Michal Neuvirth. ... Philadelphia swept the season series 3-0 and won its fifth straight at home against Buffalo and eighth in 10 games overall. ... Flyers RW Steve Downie (lower body) missed his eighth straight game. ... Philadelphia will next play at lowly Florida on Tuesday and then face Tampa Bay and Pittsburgh, which have both clinched postseason berths, on the road before Sunday's home finale against Carolina. ... Weber's goal was his first in 64 games this season.