McCoy, the former Texas star playing at the home of the Cowboys for the first time since his final college game in his home state, calmly drove the Redskins (3-5) to the winning points.
The Cowboys (6-2) had one last chance, but didn't get a first down. Romo's final pass on fourth down was knocked away by Bashaud Breeland.
Romo left after getting sacked by Keenan Robinson in the third quarter. He lay motionless for several minutes but returned for the final Dallas drive of regulation.
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