The bulk of the scoring came from running back Aaron Jones who scored all three touchdowns and ran for 93 yards.
Jamaal Williams also rushed for 63 yards as the Packers balanced the running of the ball between their two running backs.
Jones now leads the NFL in rushing touchdowns joint with Carolina's running back Christian McCaffrey, who also scored in Sunday's game. McCaffrey has now scored a TD in each of his last seven games, adding to his record amongst active players.
Davante Adams had a big second game back from his turf-toe injury with seven receptions for 118 yards including 37 and 38 yard catches in two of the Packers TD drives.
The first half
Carolina started the scoring drive in good field position. They couldn't have got off to a better start with Allen connecting with wide receiver D.J. Moore for 38 yards on the first play of the drive.
It took just four more plays for Allen to connect with Samuel for the TD.
It didn't take long for the Packers to tie the game up at seven each. On the following drive Rodgers connected with three of his wide receivers on a 75 yard drive which was finished by a five yard run by Jones.
Carolina ended the first quarter leading 10-7 thanks to a 50 yard field goal by Joey Slye.
The only points of the second quarter went to the Packers. Kyle Allen fumbled and Montravius Adams recovered for Green Bay.
Green Bay starting from their own 48 yard line due to the fumble took just 3:20 to capitalise. Davante Adams caught a 37 yard pass from Rodgers to set the Packers up at the Panthers 10 yard line.
Jones again finished the drive rushing from one yard for the score, giving the Packers a 14-10 lead at half time.
The second half
The Packers started the second half with the ball and made it count as they scored another TD to make it 21-10.
The theme of this TD drive was very much the same as their last, this one took a similar amount of time (3:10), it featured another big play from Adams, catching a 38 yard pass.
Aaron Jones also produced a big play as he ran for 28 yards on one play before again finishing the drive, this time with a 13 yard TD run for his third TD of the game.
A Mason Crosby 47 yard field goal finished off the scoring in this quarter as the Packers took a 24-10 lead into the fourth quarter.
The Panthers cut the lead to eight points in their first drive of the fourth quarter. Carolina gave the Packers a heavy dose of Christian McCaffrey who contributed 39 yards from scrimmage including a three yard TD to make it 24-16.
Carolina were unable to score again but it definitely wasn't without trying. The game ended with drama as McCaffrey from two yards out tried to run in for a TD with four seconds left but was stopped by the Packers defense.
Former Packers offensive lineman Greg Van Roten tried to pull McCaffrey over the line for the TD, however a booth review showed McCaffrey was short by one yard and the call on the field stood. The Packers won 24-16.