The Cowboys rallied after allowing a late fourth-quarter touchdown to win their third straight and improve to 6-4, keeping the pressure on the first-place New York Giants in the NFC East.
The Redskins lost their sixth straight, their longest skid since their 0-7 start in 1998. They sent the game to overtime on Rex Grossman's 4-yard fade pass to Donte' Stallworth with 14 seconds remaining in regulation.
Washington's Graham Gano missed a 52-yard field goal in overtime.
Bailey's winning kick was set up by Tony Romo's 26-yard pass to Dez Bryant.