Rodgers connected with Tom Crabtree on a 7-yard scoring strike and with James Jones on a 9-yarder in the first half en route to a 14-3 halftime lead, and his 16-yard TD toss to Brandon Jackson gave the Packers a decisive 21-10 lead in the third quarter.
Green Bay, however, had to hang on as Michael Vick rallied the Eagles late in the game, scoring a rushing touchdown with 4 minutes remaining to get the Eagles to within five points.
But his last-ditch try at a go-ahead touchdown pass in the final minute was intercepted in the end zone by Tramon Williams and the Packers advanced to play the Atlanta Falcons Saturday.
Rodgers completed 18-of-27 passes for 180 yards and James Starks racked up 123 yards on 23 carries for the Packers.
Vick connected on 20-of-36 pass attempts, amassing 292 yards with a touchdown and an interception in Philadelphia's loss.