It was a defensive battle throughout, with the teams trading punts for much of a first half that ended tied 7-7.
A Billy Cundiff field goal made it 10-7 early in the second half, but a big hit on quarterback Robert Griffin III midway through the third quarter forced him out of the game.
The Redskins didn't give up, however, with second-string quarterback Kirk Cousins finding Santana Moss for a 77-yard touchdown and a 17-14 lead.
But neither did the Falcons, who clawed their way back to take a slim 24-17 lead with three minutes left in the fourth quarter. That's all it would take, as Cousins would go on to throw interceptions on Washington's final two drives to seal the game.
Here are the Falcons' biggest winners and losers from the game.