Motte scored into an empty net with 37 seconds remaining to make it 4-2, and Alex DeBrincat scored his first goal with Ottawa, also into an empty net, with eight seconds left for the 5-2 final.
The Senators outshot the Capitals 37-12 over the last two periods.
"I feel like the first 20 (minutes) we were chipping pucks with speed, going on the forecheck and turning pucks over," Oshie said. "By the end of the first, I thought we'd backed them up a little bit. I believe we had some entries just by carrying the puck. We were shooting, we were supporting each other, and that kind of just went away. I don't know, maybe they tired us out or we got a little over-confident with the puck, or whatever it was."
NOTES:It was the first time the Senators defeated the Capitals at home since Jan. 24, 2017; Washington won the previous three here. … Tkachuk had a game-high eight shots on goal.