Newton's three rushing scores gave him 13 on the season, which established a new NFL record for rushing touchdowns by a quarterback in a single season. The previous record was held by former Patriots quarterback Steve Grogan, who ran for 12 scores in 1976 while playing a 14-game schedule.
Newton ended his day with 204 yards and one interception on 12-of-21 passing to go with 54 yards on the ground.
In addition to Newton, Jonathan Stewart had an effective day running the football, finishing with 80 yards and a touchdown on 14 carries, while DeAngelo Williams carried it 10 times for 29 yards for Carolina (4-8), which has won two straight.
Josh Johnson completed 16-of-27 passes for 229 yards, one touchdown and one interception in place of Josh Freeman, who missed the game after being injured in last week's 23-17 loss to the Tennessee Titans.
Johnson led the Bucs (4-8) in rushing with 45 yards on five carries and Dezmon Briscoe caught a touchdown pass. The Bucs have lost six consecutive games.