Backstrom scored at 3:05 of the third period to make it 2-1 off the rebound of an Ovechkin shot.
Kuznetsov scored at 7:27 when he beat Gibson short side to make it 2-2. He was trying to pass to Tom Wilson at the right post, but the puck deflected off the stick of Ducks forward Andrew Cogliano.
"We got defending too much, which brings a lot of energy out of us, and in the third we don't have that jump we need," Silfverberg said. "And they come back and win the game in OT. We've got to get back to that a little bit more of an attack mentality."
Grant gave Anaheim a 1-0 lead at 16:01 of the first period. Silfverberg scored at 7:36 of the second period five seconds into a Ducks power play to make it 2-0.
Washington is 13-2-0 at home since Nov. 2.
"We haven't played our best maybe over 60 minutes, but we find ways to win and that's all that matters," Backstrom said. "I feel like this is the time you need to get points and climb that ladder. That's what we've got to do."