The defending Super Bowl champion Packers remained unbeaten in six games this season and the Rams stayed winless in their five outings. St. Louis failed to score a touchdown after managing only one of them in each of its two previous games.
Green Bay wrapped up the victory on three straight possessions in the first half, each of them ending with a scoring throw by Rodgers.
After the Rams tried and failed to convert a fourth down from the Green Bay 41 in the final moments of the first period, the Packers drove 59 yards in five plays with Rodgers hitting James Jones for a 35-yard touchdown.
Green Bay next took over at its own 7-yard line after a St. Louis punt and Rodgers promptly found Jordy Nelson deep down the left sideline for a 93-yard score.
The Packers then marched 67 yards in 11 plays en route to a 7-yard touchdown toss from Rodgers to Donald Driver. Both teams went scoreless during the second half.
Rodgers completed 17-of-28 passes for 310 yards. He has 17 touchdown passes for the season and began the day tied for the NFL lead in that category with New England's Tom Brady.
St. Louis quarterback Sam Bradford connected on 28-of-44 pass attempts for 321 yards and an interception. The Rams converted only 3-of-13 third-down chances and were 1-of-4 on fourth down. St. Louis has been outscored by 88 points in its five losses.