Newton gained 59 rushing yards on 10 carries, including a 16-yard scoring scramble in the third quarter that put Carolina (2-5) ahead 16-6.
He also finished 18-of-23 through the air for 256 yards and no interceptions, hooking up with Brandon LaFell on a 2-yard scoring play in the fourth that upped the Panthers' advantage to 30-13.
Steve Smith was Newton's favorite target, hauling down seven passes for 143 yards.
Beck went 22-of-37 in passing efficiency for 279 yards and a TD toss to Fred Davis in the Redskins' second straight loss.
Ron Burgundy interviews Peyton Manning on SportsCenter
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'