Norman, who was coming off one of the worst games of his career, recorded his first interception since 2016 when he picked off Cam Newton early in the second quarter. On the Panthers' next possession, Norman forced a fumble, punching the ball out of rookie wide receiver DJ Moore's hands.
The Redskins' offense stalled and was able to convert those turnovers into only three points. But Norman's play certainly sparked the defense.
Smith finished with only 163 passing yards, but he did not turn the ball over. Adrian Peterson rushed 17 times for 97 yards as the Redskins (3-2) controlled the ball throughout.
The Panthers (3-2) had a golden opportunity to tie the game when Newton drove Carolina to the Washington 21-yard line with under one minute to play.
After hooking up with Christian McCaffery on first down for five yards, Newton threw three incompletions to seal the Panthers' fate.
Newton finished 27-of-40 passing for 275 yards. He threw two touchdowns and one interception.
Washington jumped out to a 14-0 first-quarter lead. Smith found tight end Vernon Davis for a 22-yard touchdown to draw first blood at 10:20 of the first quarter.
After a Panthers punt, Smith orchestrated a 12-play, 64-yard drive that resulted in a two-yard touchdown pass to Paul Richardson with 3:02 left in the first.
Dustin Hopkins' 49-yard field goal gave the Redskins a 17-0 lead with five minutes left before the intermission.
Newton finally got the Panthers on the scoreboard when he connected with Devin Funchess for a 23-yard touchdown. Graham Gano was wide left on the extra-point attempt.
The only score in the third quarter came off the foot of Gano, who connected on a 32-yard field goal to make the score 17-9.
After Hopkins was good on a 56-yard field goal, Newton drove the Panthers on a nine-play, 75-yard drive. Torrey Smith's three-yard touchdown catch and two-point conversion with 8:32 left brought Carolina to within three at 20-17.
Hopkins closed the scoring with a 29-yard field goal.
NOTES: Devin Funchess hauled in a 23-yard touchdown pass from Cam Newton -- his 19th career touchdown -- tying him with Ted Ginn Jr., for fifth-most in franchise history. ... Cam Newton tied Brett Favre for third-most total touchdowns (244) by a quarterback through his first eight seasons. Dan Marino had 246 and Peyton Manning had 253. ... Josh Norman's interception was his first since Dec. 24, 2016 against the Chicago Bears. ... Panthers safety Eric Reid took a knee during the national anthem before the game. Reid was signed as a free agent by the Panthers on Sept. 27.