Feagles, 39, broke the mark of former Minnesota Vikings and Cleveland Browns defensive end Jim Marshall, who had 282 straight appearances. The new record came after the Giants' opening possession in the first quarter.
Feagles has never missed a game since breaking into the league with the New England Patriots in 1988 and also owned the NFL's all-time mark with 1,410 career punts entering the contest.
He spent the first two of his 18-year career with the Patriots before signing with Philadelphia. He made the Pro Bowl with the Arizona Cardinals in 1995 and played five seasons with Seattle (1998-2003) before joining the Giants as a free agent.
Marshall's streak ran from 1960-1969.