The Flyers were spurred by a replenished lineup in which four players returned after spending two weeks in the NHL’s COVID-19 protocol.
They included Scott Laughton, who scored a breakaway goal to make it 3-0 late in the second period.
Elliott improved to 5-1 this season and upped his career record to 15-2-2 with four shutouts against the Sabres, including a 40-save outing in a 3-0 win on Jan. 19.
Elliott chalked up his dominance to opening his career with Ottawa, Buffalo’s traditional Atlantic Division rival.
The Sabres dropped to 2-6-1 in their past nine and played their second game without captain Jack Eichel, listed as day to day with a lower body injury.