Quarterback Aaron Rodgers threw for 229 yards and a touchdown to help guide the Packers to their sixth win of the season and keep Green Bay in touch with the Detroit Lions in the NFC North.
Both offences took a while to get going as each team traded a field goal through the opening quarter and-a-half.
The Packers finally found the end zone through AJ Dillon with just over four minutes left in the half.
A Matt Gay field goal just before half-time kept the scores close, but two quick Green Bay touchdowns in the third quarter proved enough to seal a much-needed win for the Packers.
Baker Mayfield again stood in for Matt Stafford at quarterback for the Rams, throwing for 111 yards, one touchdown and one interception.