"I have labelled myself as a pocket passer with the ability to run," Newton said.
Newton completed 21 of 34 passes for 246 yards and threw TD passes to five different receivers as Carolina stretched its regular-season win streak to 14 games, including eight straight at home.
Of the previous 15, all made the playoffs and nine have advanced to the Super Bowl, with six winning it all.
"They don't give out trophies for the regular season," Olsen said.
Carolina's defense was dominant.
"Between the fumbles and the picks, we had a couple short fields," Olsen said. "You've got to take advantage of them. We didn't sit on them. I know we scored a lot of touchdowns, and that's obviously what you're looking for."
Newton became the first Carolina quarterback in franchise history to throw four TD passes in the first half as the Panthers jumped out to a 31-14 lead.
"He has a good command of what we're doing out there," Rivera said of Newton, who has 20 TD passes this season - four shy of his career high with six games left to play.
Cousins finished 22 of 30 for 207 yards with one touchdown and one interception. He also fumbled twice on sacks. Running back Alfred Morris left the game early in the first quarter with a rib injury and did not return.
With the game tied at 14 in the second quarter, Newton led an eight-play, 92-yard touchdown drive, capping it with a 2-yard TD pass to Ginn.
"That's a 14-point turn right there," Redskins coach Jay Gruden said. "The referee made a decision, made a call, and it's not challengeable, so there's really no use talking about it."
Carolina's momentum carried into the second half as Bene Benwikere sacked Cousins on the first play from scrimmage on a cornerback blitz, jarring the ball loose and recovering at the Redskins 20. Newton found Funchess for his franchise-tying fifth TD pass of the game to give Carolina a 38-14 lead.
With a game on Thursday at Dallas, Panthers coach Ron Rivera removed most of his starters early in the fourth quarter with his team up 44-14.
"They're undefeated for a reason," Cousins said. "It doesn't just happen on accident. They have great players and a great scheme, and they have several players who've played in this system for several years. You see the fruit of that in how they've played this season."
"Last week, we felt pretty good - top of the mountain," Gruden said. "It's a humbling game."
Copyright 2015 by The Associated Press