Rodgers, the winning quarterback in the 2010 Super Bowl, scored on runs of 12 and 5 yards and the Packers held on for their first pre-season victory after losing their opening two outings.
He completed 15-of-22 passes with one interception while working the opening two quarters.
Green Bay's other scores came on field goals of 46 yards in the second period and 36 yards in the fourth quarter by Mason Crosby and a 27-yard interception return by Jamari Lattimore with 2:57 left in the game.
Cincinnati's Andy Dalton completed just 5-of-17 passes for 40 yards in first-half action. Backup quarterback Bruce Gradkowski brought the Bengals within 17-13 in the third period by throwing a 15-yard scoring pass to Marvin Jones.
The Bengals fell to 2-1 in exhibition play.