Newton finished with 204 passing yards and ran for 26 more on 10 carries as the Panthers (3-3) won for the third time in four games.
Steve Smith made five grabs for 69 yards and was on the receiving end of Newton's TD toss.
Captain Munnerlyn scored on a 45-yard interception return in the victory.
Rams quarterback Sam Bradford went 21-of-30 through the air for 255 yards with a touchdown pass before leaving the game with a leg injury.
Zac Stacy provided 87 yards of total offense and scored for St. Louis (3-4).