Rodgers had 313 yards passing and Adams had 113 yards receiving to help send Philadelphia (5-6) to its first home loss this season.
The Packers (5-6) kept their sinking playoff hopes alive but they're still two games behind the Lions (7-4) in the NFC North.
Carson Wentz had 254 yards passing, ran for a score and threw an interception. The last-place Eagles are 2-6 since a 3-0 start.
Rodgers came out firing and led the Packers on consecutive touchdown drives to start the game. Rodgers extended the opening drive by running twice for 25 yards and tossed a 12-yard TD pass to Adams for a 7-0 lead.
After the Eagles answered on Wentz's 1-yard TD run, Rodgers led another 75-yard scoring drive. He threw a perfect 20-yard TD pass to Adams to give the Packers a 14-7 lead early in the second quarter. Nolan Carroll had excellent coverage on the play, but Rodgers put the ball in a tight spot and hit Adams in stride in the back of the end zone.
Aaron Ripkowski's 1-yard TD run early in the fourth quarter extended Green Bay's lead to 24-13.
The Eagles had allowed only three touchdowns at home while outscoring opponents 108-38 in their first four games at Lincoln Financial Field.
Green Bay gave up at least 30 points in each of its previous four games, including 89 in the last two. But the defense harassed Wentz and shut down the Eagles' inconsistent offense.
Philadelphia's Caleb Sturgis kicked field goals of 48 and 50 yards while Green Bay's Mason Crosby connected from 33 and 32 yards.