Dak Prescott went 11-of-22 for 102 yards and two touchdowns, and Alfred Morris was the standout offensive player for Dallas, running for 127 yards and a touchdown on 27 carries.
Kirk Cousins threw for 251 yards and two touchdowns but also threw two interceptions and lost a fumble in what was an uneven performance.
Dez Bryant made history with a 13-yard touchdown catch in the fourth quarter. It was the 72nd touchdown reception of his career, which moved him ahead of Bob Hayes in the Cowboys' record book.
Bryant outfought Washington cornerback Bashaud Breeland to make a difficult catch, which Nick Eatman of the Cowboys' official website thought was a good way to claim the record:
The NFL shared a replay of the catch:
Prescott's numbers have dipped since Cowboys running back Ezekiel Elliott began serving his six-game suspension, which has had a ripple effect on the entire offense. Over the previous three weeks, the Cowboys had averaged 235 yards and scored 22 combined points.
Compounding matters Thursday, Prescott suffered a hand injury in the first half, and his right hand was visibly swollen later in the game, which CBSSports.com's John Breech showed:
Beating Washington will be a reason for Dallas fans to celebrate, but Prescott's injury put a small damper on the win. Dallas' offense didn't play all that much better than it did during the three-game losing streak, either.
The Cowboys gained 275 total yards and started the game with four straight punts.
Jason Witten got them on the board with an eight-yard touchdown reception at the 10:43 mark of the second quarter. Dallas added three more points as Dan Bailey connected on a 24-yard field goal after a Cousins fumble gave the Cowboys a short field.
Ryan Switzer helped give Dallas a 17-point lead when he returned a punt 83 yards to the end zone. The rookie wide receiver put his speed on display as he found an opening and blew past Washington's coverage unit. SNF on NBC shared a replay of the touchdown:
Switzer returned seven punts for touchdowns in four years at North Carolina, so former Tar Heels teammate Eric Ebron wasn't surprised by the play:
The Cowboys were scoreless in the third quarter, but their defense continued to stymie the Washington offense. Bryant's touchdown reception helped put Dallas ahead 24-7 before Josh Doctson answered back with a 14-yard touchdown grab.
Morris, who spent his first four years in the NFL in the nation's capital, capped off a 10-play, 75-yard drive with a one-yard touchdown run with 4:55 left in the fourth quarter to put the game out of reach.
Morris appeared to revel in the opportunity to play against his former team, hitting the century mark in yards for the first time since the final week of the 2015 regular season. ESPN.com's John Keim thought Morris and the Cowboys benefited from getting an early edge on Washington:
Dallas now sits in sole possession of second place in the NFC East at 6-6. While the Cowboys still have some work to do—and will be without Elliott for two more games—the schedule works out in their favor. After back-to-back Thursday games, they're off for 10 days before returning to the field.
The Cowboys have a winnable game against the New York Giants in Week 14 and follow up with the Oakland Raiders in Week 15 before Elliott returns. The Giants are 2-9 and essentially waived the white flag when they benched Eli Manning, while the Raiders rank 32nd in defensive efficiency, according to Football Outsiders.
Although Dallas still needs some help to climb into a playoff position, the postseason remains a possibility for the Cowboys.
On the other sideline, Washington's offensive line will need to get healthy fast for the 5-7 Redskins to go on a late-season run.
The team announced Morgan Moses exited the game with an ankle injury, while Trent Williams and Brandon Scherff were both listed as questionable in the injury report with knee issues. It's no coincidence the Cowboys sacked Cousins four times and limited Samaje Perine to 38 yards on 12 carries.
The Los Angeles Chargers are tied for fourth in sacks (32), so they'll test both the health and depth of Washington's offensive line when the two teams meet in Week 14.