Romo connected with Roy Williams on a play that covered 4 yards.
Dallas (10-5) also scored on a 3-yard run by Marion Barber and a 23-yard Shaun Suisham field goal.
Romo completed 25-of-38 passes for 286 yards
The Cowboys' defense held the Redskins to 218 total yards and sacked quarterback Jason Campbell three times, intercepted a pass and forced him to fumble.
Dallas still has a chance to win the title in the NFC East. The Cowboys play Philadelphia next Sunday with the winner taking the division championship.
Campbell was 24-of-39 passing for 199 yards.
Santana Moss caught eight passes for 92 yards for Washington (4-11).
2014: The Year in Music [PHOTOS]