The Redskins twice stopped Dallas on fourth down during the third period, but still couldn't move the ball in the 100th meeting between the teams.
The Cowboys were trying to clinch a playoff berth. Dallas, which holds a 58-39-2 edge in the series, would eliminate the New York Giants from postseason contention with a victory.
A win also would keep Dallas a game behind Philadelphia in the NFC East and give the Cowboys a chance to win the division title next week. The Cowboys host the Eagles in the season finale Jan. 3, and the NFL announced that kickoff has been moved to 4:15 p.m. from 1 p.m.
Jason Witten's career-long 69-yard reception set up Marion Barber's 3-yard touchdown run midway through the second quarter, giving the Cowboys a 14-0 lead at halftime.
Romo, who earlier threw a 4-yard TD pass to Roy Williams, set up Barber's score with a 69-yard completion to Witten, who got a step on free safety LaRon Landry, caught a short pass over the middle and raced down the sideline before being bumped out at the Washington 3-yard line.
On the next play, Barber took a handoff and spun into the end zone off left guard with 8 minutes left in the half.
Washington safety Reed Doughty was carted off the field with an ankle injury after picking off Romo's pass in the second quarter and didn't return. It was the first interception thrown by Romo in five games.
Terence Newman's interception set up Romo's first-quarter TD pass. Newman got his third pickoff of the season when he grabbed Jason Campbell's pass that was tipped by tight end Fred Davis.
Newman returned the ball 9 yards to the Washington 36.
Romo needed seven plays to give Dallas the lead, connecting with Williams, who beat three defenders to the far right corner of the end zone. Romo completed all three of his attempts during the drive.
The Cowboys were without special teams coordinator Joe DeCamillis, who underwent an emergency appendectomy at a Virginia hospital Sunday night. Wes Phillips, an offensive assistant and the son of coach Wade Phillips, handled the special teams units.
Before the game, a moment of silence was observed in memory of longtime Washington, D.C., sportscaster George Michael, who died on Christmas Eve at 70.