LeSean McCoy rushed the ball 29 times for a franchise-record 217 yards and scored two of the Eagles' fourth-quarter touchdowns in snowy conditions at Lincoln Financial Field in Philadelphia.
McCoy broke Steve Van Buren's record of 205 yards set in 1949.
"Records are made to be broken and it was standing for so long," McCoy said. "This is the craziest game I've played in. The best one too."
Snow began falling hours before kickoff and continued throughout the game.
With the blizzard-like conditions hampering NFL offences on Sunday, a number of teams turned to their running games and the Eagles were no exception.
Philadelphia trailed 14-6 at the end of the third but they turned it around with the help of McCoy, who scored from 40 and 57 yards.
Philadelphia hold a half-game lead over Dallas atop the NFC East and can take sole possession of the division if the Cowboys lose in Chicago on Monday.
Tom Brady threw two touchdowns passes inside the two- minute warning and the first-placed New England Patriots rallied for a 27-26 win over the Cleveland Browns.
New England, who improved to 10-3, orchestrated their third-straight comeback win but they had to do it without Rob Gronkowski.
The star tight end was carted off the field in the third quarter after suffering what is believed to be a torn ACL.
Gronkowski caught a pass from Brady before his right knee absorbed a hit by defensive back T.J. Ward.
Peyton Manning continued his run of success with 397 yards and four touchdown passes as the Denver Broncos scored 24 consecutive points in a dominating 51-28 win over the Tennessee Titans.
Matt Prater booted a NFL record 64-yard field goal for Denver, which clinched a playoff spot with the win.
In other games it was Green Bay 22 Atlanta 21, Baltimore 29 Minnesota 26, Kansas City 45 Washington 10, Tampa Bay 27 Buffalo 6, Miami 34 Pittsburgh 28, Cincinnati 42 Indianapolis 28, NY Jets 37 Oakland 27, San Francisco 19 Seattle 17, San Diego 37 NY Giants 14 and Arizona 30 St Louis 10.