The league's reigning Most Valuable Player collected his 44th career rushing touchdown on a 2-yard scamper in the second quarter of the season-opening game against the host Denver Broncos.
Newton's rushing touchdown total is the most by any quarterback since the NFL-AFL merger, breaking a tie with Hall of Famer Steve Young. He also tied Otto Graham's mark, which was set in the early 1950s.
Newton, who found wide receiver Kelvin Benjamin for a 14-yard touchdown pass midway into the first quarter, also surpassed Young for the most games (32) with both a passing and rushing score.
The top overall pick of the 2011 draft, Newton needed just 79 games to break the records of Young, who played in 169 contests over his 15-year career (1985-99).