Rodgers finished 22-of-35 for 186 yards while Donald Driver and Randall Cobb each caught a touchdown pass as resurgent Green Bay (5-3) claimed its fourth victory in five games overall.
Alex Green led the Packers' ground game, carrying the ball 22 times for 54 yards.
The Jaguars (1-6) dropped their fourth straight as Blaine Gabbert was held to 27-of-49 passing for 303 yards and a touchdown while playing through a shoulder injury.
Rashad Jennings picked up 59 yards on 17 carries for Jacksonville.
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