Rodgers had TD passes of 7 yards to Tom Crabtree, 9 to James Jones and 16 to Brandon Jackson, who used a convoy of blockers on a screen pass for the winning points midway through the third quarter.
Green Bay (11-6) then held on as Michael Vick brought Philadelphia (10-7) close, but was intercepted in the end zone by Tramon Williams in the final seconds. The Packers have won three in a row; the Eagles finished with three straight defeats.
"We have a lot of resilient guys in this locker room," Rodgers said, noting that Green Bay lost 15 players to injured reserve this season. "We have guys who believe in each other, a lot of guys we might not expect a lot from who step up, like James Starks tonight.
"It was huge the way James ran the ball, maybe the most important factor in our win," added Rodgers, who got his first playoff victory in his third season as a starter — after sitting behind Brett Favre for three years.
Green Bay began 2010 with a win at the Linc and ended the Eagles' season with another one Sunday. Now it's off to Atlanta for the divisional round.
"They have a great team over there, and they play fast," Michael Vick said after his sensational comeback season ended. "We set ourselves back. We did some things out there, still, but we just didn't do enough."