That's because Harris had 222 total return yards and Kyle Wilber forced and recovered a fumble on a sack of Griffin that left the Cowboys needing just 3 yards for a clinching score in the fourth quarter.
"Dwayne did a fantastic job," Dallas coach Jason Garrett said. "Talk about making difference-making plays in the game."
Dallas kept defending NFC East champion Washington from building any momentum after a win and a bye following an 0-3 start.
Joseph Randle, playing because running back DeMarco Murray was out with a sprained left knee, got his first career touchdown after Wilber's big play. He scored from the 1 when he stayed on his feet with a defender draped over him and was pushed into the end zone by center and Travis Frederick for a 31-16 lead.
Harris' punt return gave Dallas a 14-3 lead in the second quarter, and the big kickoff return came after Kai Forbath's third field goal pulled Washington to 14-9 in the third.
"They make my job so much easier when they block," Harris said. "I give them all the credit. We worked so hard in practice and it showed in the game."
Romo finished the job after Harris' key kickoff return. He stepped out of a potential sack and threw off balance into the corner of the end zone, where Terrance Williams got two feet down just as he made the catch and was pushed out of bounds by E.J. Biggers for a 15-yard score and a 21-9 lead.
Griffin, who was brilliant in a Thanksgiving win at the Cowboys as a rookie last year, said he was rejuvenated after a bye following Washington's first win of the season against Oakland. And he looked it.
The 2011 Heisman Trophy winner had 246 yards passing and another 77 rushing as Wsashington outgained Dallas 416 to 213.