Ottawa (8-6-6) has lost four straight. Craig Anderson made 20 saves, Ryan Dzingel scored a power-play goal at 16:37 of the second period to make it 4-1, and Mike Hoffman scored with 7:14 left in the third to make it 4-2.
Since returning from two wins against the Colorado Avalanche in the 2017 SAP NHL Global Series in Sweden on Nov. 10 and 11, Ottawa has been outscored 14-5 going 0-3-1.
"There's only one way out of this," Senators coach Guy Boucher said. "We lost four games in a row last year too. It was in the middle of the season, but whenever it is -- the beginning, middle or the end -- you've got to fight your way back. I strongly believe that our leaders care and are prepared to fight back."
Washington took a 2-0 lead with five seconds left in the first period. Alex Ovechkin, reunited on a line with Nicklas Backstrom, ended a six-game goal drought when he beat Anderson on a breakaway.
Backstrom had an assist; he had no goals and four assists in his previous 14 games.
"We understand each other, how we have to play," Ovechkin said. "Obviously, we played [together] a long time. I think it worked out perfectly today. I think [Kuznetsov's] line was good and then ours was good."
Vrana gave Washington a 1-0 lead at 15:21 of the first period.