Vinny Testaverde passed for a touchdown, Terry Glenn scored on a pass from running back Richie Anderson and Eddie George ran for another touchdown as Dallas improved to 2-1.
The 40-year-old Testaverde completed 14 of 29 passes for 214 yards.
Mark Brunell completed 25 of 43 passes for 325 yards and Rod Gardner caught nine passes, two for touchdowns, for Washington.
The Redskins (1-2) have lost 13 of their last 14 games against the Cowboys.
2014: The Year in Music [PHOTOS]